Rhonda numbers
You are encouraged to solve this task according to the task description, using any language you may know.
A positive integer n is said to be a Rhonda number to base b if the product of the base b digits of n is equal to b times the sum of n's prime factors.
These numbers were named by Kevin Brown after an acquaintance of his whose residence number was 25662, a member of the base 10 numbers with this property.
25662 is a Rhonda number to base-10. The prime factorization is 2 × 3 × 7 × 13 × 47; the product of its base-10 digits is equal to the base times the sum of its prime factors:
2 × 5 × 6 × 6 × 2 = 720 = 10 × (2 + 3 + 7 + 13 + 47)
Rhonda numbers only exist in bases that are not a prime.
Rhonda numbers to base 10 always contain at least 1 digit 5 and always contain at least 1 even digit.
- Task
- For the non-prime bases b from 2 through 16 , find and display here, on this page, at least the first 10 Rhonda numbers to base b. Display the found numbers at least in base 10.
- Stretch
- Extend out to base 36.
- See also
- Wolfram Mathworld - Rhonda numbers
- Numbers Aplenty - Rhonda numbers
- OEIS:A100968 - Integers n that are Rhonda numbers to base 4
- OEIS:A100969 - Integers n that are Rhonda numbers to base 6
- OEIS:A100970 - Integers n that are Rhonda numbers to base 8
- OEIS:A100973 - Integers n that are Rhonda numbers to base 9
- OEIS:A099542 - Rhonda numbers to base 10
- OEIS:A100971 - Integers n that are Rhonda numbers to base 12
- OEIS:A100972 - Integers n that are Rhonda numbers to base 14
- OEIS:A100974 - Integers n that are Rhonda numbers to base 15
- OEIS:A100975 - Integers n that are Rhonda numbers to base 16
ALGOL 68
BEGIN # find some Rhonda numbers: numbers n in base b such that the product #
# of the digits of n is b * the sum of the prime factors of n #
# returns the sum of the prime factors of n #
PROC factor sum = ( INT n )INT:
BEGIN
INT result := 0;
INT v := ABS n;
WHILE v > 1 AND v MOD 2 = 0 DO
result +:= 2;
v OVERAB 2
OD;
FOR f FROM 3 BY 2 WHILE v > 1 DO
WHILE v > 1 AND v MOD f = 0 DO
result +:= f;
v OVERAB f
OD
OD;
result
END # factor sum # ;
# returns the digit product of n in the specified base #
PROC digit product = ( INT n, base )INT:
IF n = 0 THEN 0
ELSE
INT result := 1;
INT v := ABS n;
WHILE v > 0 DO
result *:= v MOD base;
v OVERAB base
OD;
result
FI # digit product # ;
# returns TRUE if n is a Rhonda number in the specified base, #
# FALSE otherwise #
PROC is rhonda = ( INT n, base )BOOL: base * factor sum( n ) = digit product( n, base );
# returns TRUE if n is prime, FALSE otherwise #
PROC is prime = ( INT n )BOOL:
IF n < 3 THEN n = 2
ELIF n MOD 3 = 0 THEN n = 3
ELIF NOT ODD n THEN FALSE
ELSE
INT f := 5;
INT f2 := 25;
INT to next := 24;
BOOL is a prime := TRUE;
WHILE f2 <= n AND is a prime DO
is a prime := n MOD f /= 0;
f +:= 2;
f2 +:= to next;
to next +:= 8
OD;
is a prime
FI # is prime # ;
# returns a string representation of n in the specified base #
PROC to base string = ( INT n, base )STRING:
IF n = 0 THEN "0"
ELSE
INT under 10 = ABS "0";
INT over 9 = ABS "a" - 10;
STRING result := "";
INT v := ABS n;
WHILE v > 0 DO
INT d = v MOD base;
REPR ( d + IF d < 10 THEN under 10 ELSE over 9 FI ) +=: result;
v OVERAB base
OD;
result
FI # to base string # ;
# find the first few Rhonda numbers in non-prime bases 2 .. max base #
INT max rhonda = 10;
INT max base = 16;
FOR base FROM 2 TO max base DO
IF NOT is prime( base ) THEN
print( ( "The first ", whole( max rhonda, 0 )
, " Rhonda numbers in base ", whole( base, 0 )
, ":", newline
)
);
INT r count := 0;
[ 1 : max rhonda ]INT rhonda;
FOR n WHILE r count < max rhonda DO
IF is rhonda( n, base ) THEN
rhonda[ r count +:= 1 ] := n
FI
OD;
print( ( " in base 10:" ) );
FOR i TO max rhonda DO print( ( " ", whole( rhonda[ i ], 0 ) ) ) OD;
print( ( newline ) );
IF base /= 10 THEN
print( ( " in base ", whole( base, -2 ), ":" ) );
FOR i TO max rhonda DO print( ( " ", to base string( rhonda[ i ], base ) ) ) OD;
print( ( newline ) )
FI
FI
OD
END- Output:
The first 10 Rhonda numbers in base 4:
in base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713
in base 4: 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221
The first 10 Rhonda numbers in base 6:
in base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992
in base 6: 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132
The first 10 Rhonda numbers in base 8:
in base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956
in base 8: 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544
The first 10 Rhonda numbers in base 9:
in base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857
in base 9: 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376
The first 10 Rhonda numbers in base 10:
in base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985
The first 10 Rhonda numbers in base 12:
in base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849
in base 12: 3a8 568 2389 2689 27b6 29b4 4297 4974 5483 6a35
The first 10 Rhonda numbers in base 14:
in base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945
in base 14: 4279 6b27 76cd ab27 b7c1 1277d 173da 17547 17bc2 19437
The first 10 Rhonda numbers in base 15:
in base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758
in base 15: a97 aec 35e8 4a83 5269 5586 5a1c 5e39 735d 91a8
The first 10 Rhonda numbers in base 16:
in base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070
in base 16: 3e8 46e 1a78 3e28 4ca8 4e4b 4f83 5d8a 66b8 718e
Arturo
digs: (@`0`..`9`) ++ @`A`..`Z`
toBase: function [n,base][
join map digits.base:base n 'x -> digs\[x]
]
rhonda?: function [n,base][
(base * sum factors.prime n) = product digits.base:base n
]
nonPrime: select 2..16 'x -> not? prime? x
loop nonPrime 'npbase [
print "The first 10 Rhonda numbers, base-" ++ (to :string npbase) ++ ":"
rhondas: select.first:10 1..∞ 'z -> rhonda? z npbase
print ["In base 10 ->" join.with:", " to [:string] rhondas]
print ["In base" npbase "->" join.with:", " to [:string] map rhondas 'w -> toBase w npbase]
print ""
]
- Output:
The first 10 Rhonda numbers, base-4: In base 10 -> 10206, 11935, 12150, 16031, 45030, 94185, 113022, 114415, 191149, 244713 In base 4 -> 2133132, 2322133, 2331312, 3322133, 22333212, 112333221, 123211332, 123323233, 232222231, 323233221 The first 10 Rhonda numbers, base-6: In base 10 -> 855, 1029, 3813, 5577, 7040, 7304, 15104, 19136, 35350, 36992 In base 6 -> 3543, 4433, 25353, 41453, 52332, 53452, 153532, 224332, 431354, 443132 The first 10 Rhonda numbers, base-8: In base 10 -> 1836, 6318, 6622, 10530, 14500, 14739, 17655, 18550, 25398, 25956 In base 8 -> 3454, 14256, 14736, 24442, 34244, 34623, 42367, 44166, 61466, 62544 The first 10 Rhonda numbers, base-9: In base 10 -> 15540, 21054, 25331, 44360, 44660, 44733, 47652, 50560, 54944, 76857 In base 9 -> 23276, 31783, 37665, 66758, 67232, 67323, 72326, 76317, 83328, 126376 The first 10 Rhonda numbers, base-10: In base 10 -> 1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985 In base 10 -> 1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985 The first 10 Rhonda numbers, base-12: In base 10 -> 560, 800, 3993, 4425, 4602, 4888, 7315, 8296, 9315, 11849 In base 12 -> 3A8, 568, 2389, 2689, 27B6, 29B4, 4297, 4974, 5483, 6A35 The first 10 Rhonda numbers, base-14: In base 10 -> 11475, 18655, 20565, 29631, 31725, 45387, 58404, 58667, 59950, 63945 In base 14 -> 4279, 6B27, 76CD, AB27, B7C1, 1277D, 173DA, 17547, 17BC2, 19437 The first 10 Rhonda numbers, base-15: In base 10 -> 2392, 2472, 11468, 15873, 17424, 18126, 19152, 20079, 24388, 30758 In base 15 -> A97, AEC, 35E8, 4A83, 5269, 5586, 5A1C, 5E39, 735D, 91A8 The first 10 Rhonda numbers, base-16: In base 10 -> 1000, 1134, 6776, 15912, 19624, 20043, 20355, 23946, 26296, 29070 In base 16 -> 3E8, 46E, 1A78, 3E28, 4CA8, 4E4B, 4F83, 5D8A, 66B8, 718E
C++
#include <algorithm>
#include <cassert>
#include <iomanip>
#include <iostream>
int digit_product(int base, int n) {
int product = 1;
for (; n != 0; n /= base)
product *= n % base;
return product;
}
int prime_factor_sum(int n) {
int sum = 0;
for (; (n & 1) == 0; n >>= 1)
sum += 2;
for (int p = 3; p * p <= n; p += 2)
for (; n % p == 0; n /= p)
sum += p;
if (n > 1)
sum += n;
return sum;
}
bool is_prime(int n) {
if (n < 2)
return false;
if (n % 2 == 0)
return n == 2;
if (n % 3 == 0)
return n == 3;
for (int p = 5; p * p <= n; p += 4) {
if (n % p == 0)
return false;
p += 2;
if (n % p == 0)
return false;
}
return true;
}
bool is_rhonda(int base, int n) {
return digit_product(base, n) == base * prime_factor_sum(n);
}
std::string to_string(int base, int n) {
assert(base <= 36);
static constexpr char digits[] = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
std::string str;
for (; n != 0; n /= base)
str += digits[n % base];
std::reverse(str.begin(), str.end());
return str;
}
int main() {
const int limit = 15;
for (int base = 2; base <= 36; ++base) {
if (is_prime(base))
continue;
std::cout << "First " << limit << " Rhonda numbers to base " << base
<< ":\n";
int numbers[limit];
for (int n = 1, count = 0; count < limit; ++n) {
if (is_rhonda(base, n))
numbers[count++] = n;
}
std::cout << "In base 10:";
for (int i = 0; i < limit; ++i)
std::cout << ' ' << numbers[i];
std::cout << "\nIn base " << base << ':';
for (int i = 0; i < limit; ++i)
std::cout << ' ' << to_string(base, numbers[i]);
std::cout << "\n\n";
}
}
- Output:
First 15 Rhonda numbers to base 4: In base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713 259753 374782 392121 503773 649902 In base 4: 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221 333122221 1123133332 1133232321 1322333131 2132222232 First 15 Rhonda numbers to base 6: In base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992 41031 42009 60368 65536 67821 In base 6: 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132 513543 522253 1143252 1223224 1241553 First 15 Rhonda numbers to base 8: In base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956 30562 39215 39325 50875 51429 In base 8: 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544 73542 114457 114635 143273 144345 First 15 Rhonda numbers to base 9: In base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857 77142 83334 83694 96448 97944 In base 9: 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376 126733 136273 136723 156264 158316 First 15 Rhonda numbers to base 10: In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662 In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662 First 15 Rhonda numbers to base 12: In base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849 12028 13034 14828 15052 16264 In base 12: 3A8 568 2389 2689 27B6 29B4 4297 4974 5483 6A35 6B64 7662 86B8 8864 94B4 First 15 Rhonda numbers to base 14: In base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945 67525 68904 91245 99603 125543 In base 14: 4279 6B27 76CD AB27 B7C1 1277D 173DA 17547 17BC2 19437 1A873 1B17A 25377 28427 33A75 First 15 Rhonda numbers to base 15: In base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758 31150 33004 33550 37925 39483 In base 15: A97 AEC 35E8 4A83 5269 5586 5A1C 5E39 735D 91A8 936A 9BA4 9E1A B385 BA73 First 15 Rhonda numbers to base 16: In base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070 31906 32292 34236 34521 36465 In base 16: 3E8 46E 1A78 3E28 4CA8 4E4B 4F83 5D8A 66B8 718E 7CA2 7E24 85BC 86D9 8E71 First 15 Rhonda numbers to base 18: In base 10: 1470 3000 8918 17025 19402 20650 21120 22156 26522 36549 38354 43281 46035 48768 54229 In base 18: 49C 94C 1998 2G9F 35FG 39D4 3B36 3E6G 49F8 64E9 6A6E 77A9 7G19 8696 956D First 15 Rhonda numbers to base 20: In base 10: 1815 11050 15295 21165 22165 30702 34510 34645 42292 44165 52059 53416 65945 78430 80712 In base 20: 4AF 17CA 1I4F 2CI5 2F85 3GF2 465A 46C5 55EC 5A85 6A2J 6DAG 84H5 9G1A A1FC First 15 Rhonda numbers to base 21: In base 10: 1632 5390 8512 12992 15678 25038 29412 34017 39552 48895 49147 61376 85078 89590 91798 In base 21: 3EF C4E J67 189E 1EBC 2EG6 33EC 3E2I 45E9 55I7 5697 6D3E 93J7 9E34 9J37 First 15 Rhonda numbers to base 22: In base 10: 2695 4128 7865 28800 31710 37030 71875 74306 117760 117895 121626 126002 131427 175065 192753 In base 22: 5CB 8BE G5B 2FB2 2LB8 3AB4 6GB1 6LBC B16G B1CJ B96A BI78 C7BL G9FB I25B First 15 Rhonda numbers to base 24: In base 10: 2080 2709 3976 5628 5656 7144 8296 9030 10094 17612 20559 24616 26224 29106 31458 In base 24: 3EG 4GL 6LG 9IC 9JG C9G E9G FG6 HCE 16DK 1BGF 1IHG 1LCG 22CI 26EI First 15 Rhonda numbers to base 25: In base 10: 6764 9633 13260 22022 53382 57640 66015 69006 97014 140130 142880 144235 159724 162565 165504 In base 25: AKE FA8 L5A 1A5M 3AA7 3H5F 45FF 4AA6 655E 8O55 93F5 95JA A5DO AA2F AEK4 First 15 Rhonda numbers to base 26: In base 10: 7788 9322 9374 11160 22165 27885 34905 44785 47385 49257 62517 72709 74217 108745 132302 In base 26: BDE DKE DME GD6 16KD 1F6D 1PGD 2E6D 2I2D 2KMD 3ECD 43ED 45KD 64MD 7DIE First 15 Rhonda numbers to base 27: In base 10: 4797 11844 12078 13200 14841 17750 24320 26883 27477 46455 52750 58581 61009 61446 61500 In base 27: 6FI G6I GF9 I2O K9I O9B 169K 19NI 1AII 29JF 2I9J 2Q9I 32IG 337L 339L First 15 Rhonda numbers to base 28: In base 10: 3094 5808 5832 7462 11160 13671 27270 28194 28638 39375 39550 49500 50862 52338 52938 In base 28: 3QE 7BC 7C8 9EE E6G HC7 16LQ 17QQ 18EM 1M67 1MCE 273O 28OE 2AL6 2BEI First 15 Rhonda numbers to base 30: In base 10: 3024 3168 5115 5346 5950 6762 7750 7956 8470 9476 9576 9849 10360 11495 13035 In base 30: 3AO 3FI 5KF 5S6 6IA 7FC 8IA 8P6 9CA AFQ AJ6 AS9 BFA CN5 EEF First 15 Rhonda numbers to base 32: In base 10: 1944 3600 13520 15876 16732 16849 25410 25752 28951 47472 49610 50968 61596 64904 74005 In base 32: 1SO 3GG D6G FG4 GAS GEH OQ2 P4O S8N 1EBG 1GEA 1HOO 1S4S 1VC8 288L First 15 Rhonda numbers to base 33: In base 10: 756 7040 7568 13826 24930 30613 59345 63555 64372 131427 227840 264044 313709 336385 344858 In base 33: MU 6FB 6VB CMW MTF S3M 1LGB 1PBU 1Q3M 3LML 6B78 7BFB 8O2B 9BTG 9JM8 First 15 Rhonda numbers to base 34: In base 10: 5661 14161 15620 16473 22185 37145 125579 134692 135405 138472 140369 177086 250665 255552 295614 In base 34: 4UH C8H DHE E8H J6H W4H 36LH 3EHI 3F4H 3HQO 3JEH 4H6E 6CSH 6H28 7HOI First 15 Rhonda numbers to base 35: In base 10: 8232 9476 9633 18634 30954 41905 52215 52440 56889 61992 62146 66339 98260 102180 103305 In base 35: 6P7 7PQ 7U8 F7E P9E Y7A 17LU 17SA 1BFE 1FL7 1FPL 1J5E 2A7F 2DEF 2EBK First 15 Rhonda numbers to base 36: In base 10: 1000 4800 5670 8190 10998 12412 13300 15750 16821 23016 51612 52734 67744 70929 75030 In base 36: RS 3PC 4DI 6BI 8HI 9KS A9G C5I CZ9 HRC 13TO 14OU 1G9S 1IQ9 1LW6
Factor
USING: formatting grouping io kernel lists lists.lazy math
math.parser math.primes math.primes.factors prettyprint ranges
sequences sequences.extras ;
: rhonda? ( n base -- ? )
[ [ >base 1 group ] keep '[ _ base> ] map-product ]
[ swap factors sum * ] 2bi = ;
: rhonda ( base -- list ) 1 lfrom swap '[ _ rhonda? ] lfilter ;
: list. ( list base -- ) '[ _ >base write bl ] leach nl ;
:: rhonda. ( base -- )
15 base rhonda ltake :> r
base "First 15 Rhonda numbers to base %d:\n" printf
"In base 10: " write r 10 list.
base "In base %d: " printf r base list. ;
2 36 [a..b] [ prime? not ] filter [ rhonda. nl ] each
- Output:
First 15 Rhonda numbers to base 4: In base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713 259753 374782 392121 503773 649902 In base 4: 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221 333122221 1123133332 1133232321 1322333131 2132222232 First 15 Rhonda numbers to base 6: In base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992 41031 42009 60368 65536 67821 In base 6: 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132 513543 522253 1143252 1223224 1241553 First 15 Rhonda numbers to base 8: In base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956 30562 39215 39325 50875 51429 In base 8: 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544 73542 114457 114635 143273 144345 First 15 Rhonda numbers to base 9: In base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857 77142 83334 83694 96448 97944 In base 9: 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376 126733 136273 136723 156264 158316 First 15 Rhonda numbers to base 10: In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662 In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662 First 15 Rhonda numbers to base 12: In base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849 12028 13034 14828 15052 16264 In base 12: 3a8 568 2389 2689 27b6 29b4 4297 4974 5483 6a35 6b64 7662 86b8 8864 94b4 First 15 Rhonda numbers to base 14: In base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945 67525 68904 91245 99603 125543 In base 14: 4279 6b27 76cd ab27 b7c1 1277d 173da 17547 17bc2 19437 1a873 1b17a 25377 28427 33a75 First 15 Rhonda numbers to base 15: In base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758 31150 33004 33550 37925 39483 In base 15: a97 aec 35e8 4a83 5269 5586 5a1c 5e39 735d 91a8 936a 9ba4 9e1a b385 ba73 First 15 Rhonda numbers to base 16: In base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070 31906 32292 34236 34521 36465 In base 16: 3e8 46e 1a78 3e28 4ca8 4e4b 4f83 5d8a 66b8 718e 7ca2 7e24 85bc 86d9 8e71 First 15 Rhonda numbers to base 18: In base 10: 1470 3000 8918 17025 19402 20650 21120 22156 26522 36549 38354 43281 46035 48768 54229 In base 18: 49c 94c 1998 2g9f 35fg 39d4 3b36 3e6g 49f8 64e9 6a6e 77a9 7g19 8696 956d First 15 Rhonda numbers to base 20: In base 10: 1815 11050 15295 21165 22165 30702 34510 34645 42292 44165 52059 53416 65945 78430 80712 In base 20: 4af 17ca 1i4f 2ci5 2f85 3gf2 465a 46c5 55ec 5a85 6a2j 6dag 84h5 9g1a a1fc First 15 Rhonda numbers to base 21: In base 10: 1632 5390 8512 12992 15678 25038 29412 34017 39552 48895 49147 61376 85078 89590 91798 In base 21: 3ef c4e j67 189e 1ebc 2eg6 33ec 3e2i 45e9 55i7 5697 6d3e 93j7 9e34 9j37 First 15 Rhonda numbers to base 22: In base 10: 2695 4128 7865 28800 31710 37030 71875 74306 117760 117895 121626 126002 131427 175065 192753 In base 22: 5cb 8be g5b 2fb2 2lb8 3ab4 6gb1 6lbc b16g b1cj b96a bi78 c7bl g9fb i25b First 15 Rhonda numbers to base 24: In base 10: 2080 2709 3976 5628 5656 7144 8296 9030 10094 17612 20559 24616 26224 29106 31458 In base 24: 3eg 4gl 6lg 9ic 9jg c9g e9g fg6 hce 16dk 1bgf 1ihg 1lcg 22ci 26ei First 15 Rhonda numbers to base 25: In base 10: 6764 9633 13260 22022 53382 57640 66015 69006 97014 140130 142880 144235 159724 162565 165504 In base 25: ake fa8 l5a 1a5m 3aa7 3h5f 45ff 4aa6 655e 8o55 93f5 95ja a5do aa2f aek4 First 15 Rhonda numbers to base 26: In base 10: 7788 9322 9374 11160 22165 27885 34905 44785 47385 49257 62517 72709 74217 108745 132302 In base 26: bde dke dme gd6 16kd 1f6d 1pgd 2e6d 2i2d 2kmd 3ecd 43ed 45kd 64md 7die First 15 Rhonda numbers to base 27: In base 10: 4797 11844 12078 13200 14841 17750 24320 26883 27477 46455 52750 58581 61009 61446 61500 In base 27: 6fi g6i gf9 i2o k9i o9b 169k 19ni 1aii 29jf 2i9j 2q9i 32ig 337l 339l First 15 Rhonda numbers to base 28: In base 10: 3094 5808 5832 7462 11160 13671 27270 28194 28638 39375 39550 49500 50862 52338 52938 In base 28: 3qe 7bc 7c8 9ee e6g hc7 16lq 17qq 18em 1m67 1mce 273o 28oe 2al6 2bei First 15 Rhonda numbers to base 30: In base 10: 3024 3168 5115 5346 5950 6762 7750 7956 8470 9476 9576 9849 10360 11495 13035 In base 30: 3ao 3fi 5kf 5s6 6ia 7fc 8ia 8p6 9ca afq aj6 as9 bfa cn5 eef First 15 Rhonda numbers to base 32: In base 10: 1944 3600 13520 15876 16732 16849 25410 25752 28951 47472 49610 50968 61596 64904 74005 In base 32: 1so 3gg d6g fg4 gas geh oq2 p4o s8n 1ebg 1gea 1hoo 1s4s 1vc8 288l First 15 Rhonda numbers to base 33: In base 10: 756 7040 7568 13826 24930 30613 59345 63555 64372 131427 227840 264044 313709 336385 344858 In base 33: mu 6fb 6vb cmw mtf s3m 1lgb 1pbu 1q3m 3lml 6b78 7bfb 8o2b 9btg 9jm8 First 15 Rhonda numbers to base 34: In base 10: 5661 14161 15620 16473 22185 37145 125579 134692 135405 138472 140369 177086 250665 255552 295614 In base 34: 4uh c8h dhe e8h j6h w4h 36lh 3ehi 3f4h 3hqo 3jeh 4h6e 6csh 6h28 7hoi First 15 Rhonda numbers to base 35: In base 10: 8232 9476 9633 18634 30954 41905 52215 52440 56889 61992 62146 66339 98260 102180 103305 In base 35: 6p7 7pq 7u8 f7e p9e y7a 17lu 17sa 1bfe 1fl7 1fpl 1j5e 2a7f 2def 2ebk First 15 Rhonda numbers to base 36: In base 10: 1000 4800 5670 8190 10998 12412 13300 15750 16821 23016 51612 52734 67744 70929 75030 In base 36: rs 3pc 4di 6bi 8hi 9ks a9g c5i cz9 hrc 13to 14ou 1g9s 1iq9 1lw6
FreeBASIC
'#include "isprime.bas"
Function FactorSum(n As Uinteger) As Uinteger
Dim As Uinteger result = 0
Dim As Uinteger v = Abs(n)
While v > 1 And v Mod 2 = 0
result += 2
v \= 2
Wend
For f As Uinteger = 3 To v Step 2
While v > 1 And v Mod f = 0
result += f
v \= f
Wend
Next f
Return result
End Function
Function DigitProduct(n As Uinteger, base_ As Uinteger) As Uinteger
If n = 0 Then Return 0
Dim As Uinteger result = 1
Dim As Uinteger v = Abs(n)
While v > 0
result *= v Mod base_
v \= base_
Wend
Return result
End Function
Function isRhonda(n As Uinteger, base_ As Uinteger) As Uinteger
Return base_ * FactorSum(n) = DigitProduct(n, base_)
End Function
Function ToBaseString(n As Uinteger, base_ As Uinteger) As String
If n = 0 Then Return "0"
Dim As Uinteger under10 = Asc("0")
Dim As Uinteger over9 = Asc("a") - 10
Dim As String result = ""
Dim As Uinteger v = Abs(n)
While v > 0
Dim As Uinteger d = v Mod base_
result = Chr(d + Iif(d < 10, under10, over9)) + result
v \= base_
Wend
Return result
End Function
Dim As Uinteger maxRhonda = 10, maxBase = 16
For base_ As Uinteger = 2 To maxBase
If Not isPrime(base_) Then
Print "The first "; maxRhonda; " Rhonda numbers in base "; base_; ":"
Dim As Uinteger rCount = 0
Dim As Uinteger rhonda(1 To maxRhonda)
Dim As Uinteger n = 1
While rCount < maxRhonda
If isRhonda(n, base_) Then
rCount += 1
rhonda(rCount) = n
End If
n += 1
Wend
Print " in base 10: ";
For i As Uinteger = 1 To maxRhonda
Print " "; rhonda(i);
Next i
Print
If base_ <> 10 Then
Print Using " in base ##: "; base_;
For i As Uinteger = 1 To maxRhonda
Print " "; ToBaseString(rhonda(i), base_);
Next i
Print
End If
End If
Next base_
Sleep
- Output:
Same as ALGOL 68 entry.
Go
package main
import (
"fmt"
"rcu"
"strconv"
)
func contains(a []int, n int) bool {
for _, e := range a {
if e == n {
return true
}
}
return false
}
func main() {
for b := 2; b <= 36; b++ {
if rcu.IsPrime(b) {
continue
}
count := 0
var rhonda []int
for n := 1; count < 15; n++ {
digits := rcu.Digits(n, b)
if !contains(digits, 0) {
var anyEven = false
for _, d := range digits {
if d%2 == 0 {
anyEven = true
break
}
}
if b != 10 || (contains(digits, 5) && anyEven) {
calc1 := 1
for _, d := range digits {
calc1 *= d
}
calc2 := b * rcu.SumInts(rcu.PrimeFactors(n))
if calc1 == calc2 {
rhonda = append(rhonda, n)
count++
}
}
}
}
if len(rhonda) > 0 {
fmt.Printf("\nFirst 15 Rhonda numbers in base %d:\n", b)
rhonda2 := make([]string, len(rhonda))
counts2 := make([]int, len(rhonda))
for i, r := range rhonda {
rhonda2[i] = fmt.Sprintf("%d", r)
counts2[i] = len(rhonda2[i])
}
rhonda3 := make([]string, len(rhonda))
counts3 := make([]int, len(rhonda))
for i, r := range rhonda {
rhonda3[i] = strconv.FormatInt(int64(r), b)
counts3[i] = len(rhonda3[i])
}
maxLen2 := rcu.MaxInts(counts2)
maxLen3 := rcu.MaxInts(counts3)
maxLen := maxLen2
if maxLen3 > maxLen {
maxLen = maxLen3
}
maxLen++
fmt.Printf("In base 10: %*s\n", maxLen, rhonda2)
fmt.Printf("In base %-2d: %*s\n", b, maxLen, rhonda3)
}
}
}
- Output:
First 15 Rhonda numbers in base 4: In base 10: [ 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713 259753 374782 392121 503773 649902] In base 4 : [ 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221 333122221 1123133332 1133232321 1322333131 2132222232] First 15 Rhonda numbers in base 6: In base 10: [ 855 1029 3813 5577 7040 7304 15104 19136 35350 36992 41031 42009 60368 65536 67821] In base 6 : [ 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132 513543 522253 1143252 1223224 1241553] First 15 Rhonda numbers in base 8: In base 10: [ 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956 30562 39215 39325 50875 51429] In base 8 : [ 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544 73542 114457 114635 143273 144345] First 15 Rhonda numbers in base 9: In base 10: [ 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857 77142 83334 83694 96448 97944] In base 9 : [ 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376 126733 136273 136723 156264 158316] First 15 Rhonda numbers in base 10: In base 10: [ 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662] In base 10: [ 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662] First 15 Rhonda numbers in base 12: In base 10: [ 560 800 3993 4425 4602 4888 7315 8296 9315 11849 12028 13034 14828 15052 16264] In base 12: [ 3a8 568 2389 2689 27b6 29b4 4297 4974 5483 6a35 6b64 7662 86b8 8864 94b4] First 15 Rhonda numbers in base 14: In base 10: [ 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945 67525 68904 91245 99603 125543] In base 14: [ 4279 6b27 76cd ab27 b7c1 1277d 173da 17547 17bc2 19437 1a873 1b17a 25377 28427 33a75] First 15 Rhonda numbers in base 15: In base 10: [ 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758 31150 33004 33550 37925 39483] In base 15: [ a97 aec 35e8 4a83 5269 5586 5a1c 5e39 735d 91a8 936a 9ba4 9e1a b385 ba73] First 15 Rhonda numbers in base 16: In base 10: [ 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070 31906 32292 34236 34521 36465] In base 16: [ 3e8 46e 1a78 3e28 4ca8 4e4b 4f83 5d8a 66b8 718e 7ca2 7e24 85bc 86d9 8e71] First 15 Rhonda numbers in base 18: In base 10: [ 1470 3000 8918 17025 19402 20650 21120 22156 26522 36549 38354 43281 46035 48768 54229] In base 18: [ 49c 94c 1998 2g9f 35fg 39d4 3b36 3e6g 49f8 64e9 6a6e 77a9 7g19 8696 956d] First 15 Rhonda numbers in base 20: In base 10: [ 1815 11050 15295 21165 22165 30702 34510 34645 42292 44165 52059 53416 65945 78430 80712] In base 20: [ 4af 17ca 1i4f 2ci5 2f85 3gf2 465a 46c5 55ec 5a85 6a2j 6dag 84h5 9g1a a1fc] First 15 Rhonda numbers in base 21: In base 10: [ 1632 5390 8512 12992 15678 25038 29412 34017 39552 48895 49147 61376 85078 89590 91798] In base 21: [ 3ef c4e j67 189e 1ebc 2eg6 33ec 3e2i 45e9 55i7 5697 6d3e 93j7 9e34 9j37] First 15 Rhonda numbers in base 22: In base 10: [ 2695 4128 7865 28800 31710 37030 71875 74306 117760 117895 121626 126002 131427 175065 192753] In base 22: [ 5cb 8be g5b 2fb2 2lb8 3ab4 6gb1 6lbc b16g b1cj b96a bi78 c7bl g9fb i25b] First 15 Rhonda numbers in base 24: In base 10: [ 2080 2709 3976 5628 5656 7144 8296 9030 10094 17612 20559 24616 26224 29106 31458] In base 24: [ 3eg 4gl 6lg 9ic 9jg c9g e9g fg6 hce 16dk 1bgf 1ihg 1lcg 22ci 26ei] First 15 Rhonda numbers in base 25: In base 10: [ 6764 9633 13260 22022 53382 57640 66015 69006 97014 140130 142880 144235 159724 162565 165504] In base 25: [ ake fa8 l5a 1a5m 3aa7 3h5f 45ff 4aa6 655e 8o55 93f5 95ja a5do aa2f aek4] First 15 Rhonda numbers in base 26: In base 10: [ 7788 9322 9374 11160 22165 27885 34905 44785 47385 49257 62517 72709 74217 108745 132302] In base 26: [ bde dke dme gd6 16kd 1f6d 1pgd 2e6d 2i2d 2kmd 3ecd 43ed 45kd 64md 7die] First 15 Rhonda numbers in base 27: In base 10: [ 4797 11844 12078 13200 14841 17750 24320 26883 27477 46455 52750 58581 61009 61446 61500] In base 27: [ 6fi g6i gf9 i2o k9i o9b 169k 19ni 1aii 29jf 2i9j 2q9i 32ig 337l 339l] First 15 Rhonda numbers in base 28: In base 10: [ 3094 5808 5832 7462 11160 13671 27270 28194 28638 39375 39550 49500 50862 52338 52938] In base 28: [ 3qe 7bc 7c8 9ee e6g hc7 16lq 17qq 18em 1m67 1mce 273o 28oe 2al6 2bei] First 15 Rhonda numbers in base 30: In base 10: [ 3024 3168 5115 5346 5950 6762 7750 7956 8470 9476 9576 9849 10360 11495 13035] In base 30: [ 3ao 3fi 5kf 5s6 6ia 7fc 8ia 8p6 9ca afq aj6 as9 bfa cn5 eef] First 15 Rhonda numbers in base 32: In base 10: [ 1944 3600 13520 15876 16732 16849 25410 25752 28951 47472 49610 50968 61596 64904 74005] In base 32: [ 1so 3gg d6g fg4 gas geh oq2 p4o s8n 1ebg 1gea 1hoo 1s4s 1vc8 288l] First 15 Rhonda numbers in base 33: In base 10: [ 756 7040 7568 13826 24930 30613 59345 63555 64372 131427 227840 264044 313709 336385 344858] In base 33: [ mu 6fb 6vb cmw mtf s3m 1lgb 1pbu 1q3m 3lml 6b78 7bfb 8o2b 9btg 9jm8] First 15 Rhonda numbers in base 34: In base 10: [ 5661 14161 15620 16473 22185 37145 125579 134692 135405 138472 140369 177086 250665 255552 295614] In base 34: [ 4uh c8h dhe e8h j6h w4h 36lh 3ehi 3f4h 3hqo 3jeh 4h6e 6csh 6h28 7hoi] First 15 Rhonda numbers in base 35: In base 10: [ 8232 9476 9633 18634 30954 41905 52215 52440 56889 61992 62146 66339 98260 102180 103305] In base 35: [ 6p7 7pq 7u8 f7e p9e y7a 17lu 17sa 1bfe 1fl7 1fpl 1j5e 2a7f 2def 2ebk] First 15 Rhonda numbers in base 36: In base 10: [ 1000 4800 5670 8190 10998 12412 13300 15750 16821 23016 51612 52734 67744 70929 75030] In base 36: [ rs 3pc 4di 6bi 8hi 9ks a9g c5i cz9 hrc 13to 14ou 1g9s 1iq9 1lw6]
J
tobase=: (a.{~;48 97(+ i.)each 10 26) {~ #.inv
isrhonda=: (*/@:(#.inv) = (* +/@q:))"0
task=: {{
for_base.(#~ 0=1&p:) }.1+i.36 do.
k=.i.0
block=. 1+i.1e4
while. 15>#k do.
k=. k, block#~ base isrhonda block
block=. block+1e4
end.
echo ''
echo 'First 15 Rhondas in',b=.' base ',':',~":base
echo 'In base 10: ',":15{.k
echo 'In',;:inv b;base tobase each 15{.k
end.
}}
task''
- Output:
First 15 Rhondas in base 4: In base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713 259753 374782 392121 503773 649902 In base 4: 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221 333122221 1123133332 1133232321 1322333131 2132222232 First 15 Rhondas in base 6: In base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992 41031 42009 60368 65536 67821 In base 6: 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132 513543 522253 1143252 1223224 1241553 First 15 Rhondas in base 8: In base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956 30562 39215 39325 50875 51429 In base 8: 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544 73542 114457 114635 143273 144345 First 15 Rhondas in base 9: In base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857 77142 83334 83694 96448 97944 In base 9: 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376 126733 136273 136723 156264 158316 First 15 Rhondas in base 10: In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662 In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662 First 15 Rhondas in base 12: In base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849 12028 13034 14828 15052 16264 In base 12: 3a8 568 2389 2689 27b6 29b4 4297 4974 5483 6a35 6b64 7662 86b8 8864 94b4 First 15 Rhondas in base 14: In base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945 67525 68904 91245 99603 125543 In base 14: 4279 6b27 76cd ab27 b7c1 1277d 173da 17547 17bc2 19437 1a873 1b17a 25377 28427 33a75 First 15 Rhondas in base 15: In base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758 31150 33004 33550 37925 39483 In base 15: a97 aec 35e8 4a83 5269 5586 5a1c 5e39 735d 91a8 936a 9ba4 9e1a b385 ba73 First 15 Rhondas in base 16: In base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070 31906 32292 34236 34521 36465 In base 16: 3e8 46e 1a78 3e28 4ca8 4e4b 4f83 5d8a 66b8 718e 7ca2 7e24 85bc 86d9 8e71 First 15 Rhondas in base 18: In base 10: 1470 3000 8918 17025 19402 20650 21120 22156 26522 36549 38354 43281 46035 48768 54229 In base 18: 49c 94c 1998 2g9f 35fg 39d4 3b36 3e6g 49f8 64e9 6a6e 77a9 7g19 8696 956d First 15 Rhondas in base 20: In base 10: 1815 11050 15295 21165 22165 30702 34510 34645 42292 44165 52059 53416 65945 78430 80712 In base 20: 4af 17ca 1i4f 2ci5 2f85 3gf2 465a 46c5 55ec 5a85 6a2j 6dag 84h5 9g1a a1fc First 15 Rhondas in base 21: In base 10: 1632 5390 8512 12992 15678 25038 29412 34017 39552 48895 49147 61376 85078 89590 91798 In base 21: 3ef c4e j67 189e 1ebc 2eg6 33ec 3e2i 45e9 55i7 5697 6d3e 93j7 9e34 9j37 First 15 Rhondas in base 22: In base 10: 2695 4128 7865 28800 31710 37030 71875 74306 117760 117895 121626 126002 131427 175065 192753 In base 22: 5cb 8be g5b 2fb2 2lb8 3ab4 6gb1 6lbc b16g b1cj b96a bi78 c7bl g9fb i25b First 15 Rhondas in base 24: In base 10: 2080 2709 3976 5628 5656 7144 8296 9030 10094 17612 20559 24616 26224 29106 31458 In base 24: 3eg 4gl 6lg 9ic 9jg c9g e9g fg6 hce 16dk 1bgf 1ihg 1lcg 22ci 26ei First 15 Rhondas in base 25: In base 10: 6764 9633 13260 22022 53382 57640 66015 69006 97014 140130 142880 144235 159724 162565 165504 In base 25: ake fa8 l5a 1a5m 3aa7 3h5f 45ff 4aa6 655e 8o55 93f5 95ja a5do aa2f aek4 First 15 Rhondas in base 26: In base 10: 7788 9322 9374 11160 22165 27885 34905 44785 47385 49257 62517 72709 74217 108745 132302 In base 26: bde dke dme gd6 16kd 1f6d 1pgd 2e6d 2i2d 2kmd 3ecd 43ed 45kd 64md 7die First 15 Rhondas in base 27: In base 10: 4797 11844 12078 13200 14841 17750 24320 26883 27477 46455 52750 58581 61009 61446 61500 In base 27: 6fi g6i gf9 i2o k9i o9b 169k 19ni 1aii 29jf 2i9j 2q9i 32ig 337l 339l First 15 Rhondas in base 28: In base 10: 3094 5808 5832 7462 11160 13671 27270 28194 28638 39375 39550 49500 50862 52338 52938 In base 28: 3qe 7bc 7c8 9ee e6g hc7 16lq 17qq 18em 1m67 1mce 273o 28oe 2al6 2bei First 15 Rhondas in base 30: In base 10: 3024 3168 5115 5346 5950 6762 7750 7956 8470 9476 9576 9849 10360 11495 13035 In base 30: 3ao 3fi 5kf 5s6 6ia 7fc 8ia 8p6 9ca afq aj6 as9 bfa cn5 eef First 15 Rhondas in base 32: In base 10: 1944 3600 13520 15876 16732 16849 25410 25752 28951 47472 49610 50968 61596 64904 74005 In base 32: 1so 3gg d6g fg4 gas geh oq2 p4o s8n 1ebg 1gea 1hoo 1s4s 1vc8 288l First 15 Rhondas in base 33: In base 10: 756 7040 7568 13826 24930 30613 59345 63555 64372 131427 227840 264044 313709 336385 344858 In base 33: mu 6fb 6vb cmw mtf s3m 1lgb 1pbu 1q3m 3lml 6b78 7bfb 8o2b 9btg 9jm8 First 15 Rhondas in base 34: In base 10: 5661 14161 15620 16473 22185 37145 125579 134692 135405 138472 140369 177086 250665 255552 295614 In base 34: 4uh c8h dhe e8h j6h w4h 36lh 3ehi 3f4h 3hqo 3jeh 4h6e 6csh 6h28 7hoi First 15 Rhondas in base 35: In base 10: 8232 9476 9633 18634 30954 41905 52215 52440 56889 61992 62146 66339 98260 102180 103305 In base 35: 6p7 7pq 7u8 f7e p9e y7a 17lu 17sa 1bfe 1fl7 1fpl 1j5e 2a7f 2def 2ebk First 15 Rhondas in base 36: In base 10: 1000 4800 5670 8190 10998 12412 13300 15750 16821 23016 51612 52734 67744 70929 75030 In base 36: rs 3pc 4di 6bi 8hi 9ks a9g c5i cz9 hrc 13to 14ou 1g9s 1iq9 1lw6
Hoon
Library file (e.g. /lib/rhonda.hoon):
::
:: A library for producing Rhonda numbers and testing if numbers are Rhonda.
::
:: A number is Rhonda if the product of its digits of in base b equals
:: the product of the base b and the sum of its prime factors.
:: see also: https://mathworld.wolfram.com/RhondaNumber.html
::
=<
::
|%
:: +check: test whether the number n is Rhonda to base b
::
++ check
|= [b=@ud n=@ud]
^- ?
~_ leaf+"base b must be >= 2"
?> (gte b 2)
~_ leaf+"candidate number n must be >= 2"
?> (gte n 2)
::
.= (roll (base-digits b n) mul)
%+ mul
b
(roll (prime-factors n) add)
:: +series: produce the first n numbers which are Rhonda in base b
::
:: produce ~ if base b has no Rhonda numbers
::
++ series
|= [b=@ud n=@ud]
^- (list @ud)
~_ leaf+"base b must be >= 2"
?> (gte b 2)
::
?: =((prime-factors b) ~[b])
~
=/ candidate=@ud 2
=+ rhondas=*(list @ud)
|-
?: =(n 0)
(flop rhondas)
=/ is-rhonda=? (check b candidate)
%= $
rhondas ?:(is-rhonda [candidate rhondas] rhondas)
n ?:(is-rhonda (dec n) n)
candidate +(candidate)
==
--
::
|%
:: +base-digits: produce a list of the digits of n represented in base b
::
:: This arm has two behaviors which may be at first surprising, but do not
:: matter for the purposes of the ++check and ++series arms, and allow for
:: some simplifications to its implementation.
:: - crashes on n=0
:: - orders the list of digits with least significant digits first
::
:: ex: (base-digits 4 10.206) produces ~[2 3 1 3 3 1 2]
::
++ base-digits
|= [b=@ud n=@ud]
^- (list @ud)
?> (gte b 2)
?< =(n 0)
::
|-
?: =(n 0)
~
:- (mod n b)
$(n (div n b))
:: +prime-factors: produce a list of the prime factors of n
::
:: by trial division
:: n must be >= 2
:: if n is prime, produce ~[n]
:: ex: (prime-factors 10.206) produces ~[7 3 3 3 3 3 3 2]
::
++ prime-factors
|= [n=@ud]
^- (list @ud)
?> (gte n 2)
::
=+ factors=*(list @ud)
=/ wheel new-wheel
:: test candidates as produced by the wheel, not exceeding sqrt(n)
::
|-
=^ candidate wheel (next:wheel)
?. (lte (mul candidate candidate) n)
?:((gth n 1) [n factors] factors)
|-
?: =((mod n candidate) 0)
:: repeat the prime factor as many times as possible
::
$(factors [candidate factors], n (div n candidate))
^$
:: +new-wheel: a door for generating numbers that may be prime
::
:: This uses wheel factorization with a basis of {2, 3, 5} to limit the
:: number of composites produced. It produces numbers in increasing order
:: starting from 2.
::
++ new-wheel
=/ fixed=(list @ud) ~[2 3 5 7]
=/ skips=(list @ud) ~[4 2 4 2 4 6 2 6]
=/ lent-fixed=@ud (lent fixed)
=/ lent-skips=@ud (lent skips)
::
|_ [current=@ud fixed-i=@ud skips-i=@ud]
:: +next: produce the next number and the new wheel state
::
++ next
|.
:: Exhaust the numbers in fixed. Then calculate successive values by
:: cycling through skips and increasing from the previous number by
:: the current skip-value.
::
=/ fixed-done=? =(fixed-i lent-fixed)
=/ next-fixed-i ?:(fixed-done fixed-i +(fixed-i))
=/ next-skips-i ?:(fixed-done (mod +(skips-i) lent-skips) skips-i)
=/ next
?. fixed-done
(snag fixed-i fixed)
(add current (snag skips-i skips))
:- next
+.$(current next, fixed-i next-fixed-i, skips-i next-skips-i)
--
--Script file ("generator") (e.g. /gen/rhonda.hoon):
/+ *rhonda
:- %say
|= [* [base=@ud many=@ud ~] ~]
:- %noun
(series base many)Alternative library file using map (associative array):
|%
++ check
|= [n=@ud base=@ud]
:: if base is prime, automatic no
::
?: =((~(gut by (prime-map +(base))) base 0) 0)
%.n
:: if not multiply the digits and compare to base x sum of factors
::
?: =((roll (digits [base n]) mul) (mul base (roll (factor n) add)))
%.y
%.n
++ series
|= [base=@ud many=@ud]
=/ rhondas *(list @ud)
?: =((~(gut by (prime-map +(base))) base 0) 0)
rhondas
=/ itr 1
|-
?: =((lent rhondas) many)
(flop rhondas)
?: =((check itr base) %.n)
$(itr +(itr))
$(rhondas [itr rhondas], itr +(itr))
:: digits: gives the list of digits of a number in a base
::
:: We strip digits least to most significant.
:: The least significant digit (lsd) of n in base b is just n mod b.
:: Subtract the lsd, divide by b, and repeat.
:: To know when to stop, we need to know how many digits there are.
++ digits
|= [base=@ud num=@ud]
^- (list @ud)
|-
=/ modulus=@ud (mod num base)
?: =((num-digits base num) 1)
~[modulus]
[modulus $(num (div (sub num modulus) base))]
:: num-digits: gives the number of digits of a number in a base
::
:: Simple idea: k is the number of digits of n in base b if and
:: only if k is the smallest number such that b^k > n.
++ num-digits
|= [base=@ud num=@ud]
^- @ud
=/ digits=@ud 1
|-
?: (gth (pow base digits) num)
digits
$(digits +(digits))
:: factor: produce a list of prime factors
::
:: The idea is to identify "small factors" of n, i.e. prime factors less than
:: the square root. We then divide n by these factors to reduce the
:: magnitude of n. It's easy to argue that after this is done, we obtain 1
:: or the largest prime factor.
::
++ factor
|= n=@ud
^- (list @ud)
?: ?|(=(n 0) =(n 1))
~[n]
=/ factorization *(list @ud)
:: produce primes less than or equal to root n
::
=/ root (sqrt n)
=/ primes (prime-map +(root))
:: itr = iterate; we want to iterate through the primes less than root n
::
=/ itr 2
|-
?: =(itr +(root))
:: if n is now 1 we're done
::
?: =(n 1)
factorization
:: otherwise it's now the original n's largest primes factor
::
[n factorization]
:: if itr not prime move on
::
?: =((~(gut by primes) itr 0) 1)
$(itr +(itr))
:: if it is prime, divide out by the highest power that divides num
::
?: =((mod n itr) 0)
$(n (div n itr), factorization [itr factorization])
:: once done, move to next prime
::
$(itr +(itr))
:: sqrt: gives the integer square root of a number
::
:: It's based on an algorithm that predates the Greeks:
:: To find the square root of A, think of A as an area.
:: Guess the side of the square x. Compute the other side y = A/x.
:: If x is an over/underestimate then y is an under/overestimate.
:: So (x+y)/2 is the average of an over and underestimate, thus better than x.
:: Repeatedly doing x --> (x + A/x)/2 converges to sqrt(A).
::
:: This algorithm is the same but with integer valued operations.
:: The algorithm either converges to the integer square root and repeats,
:: or gets trapped in a two-cycle of adjacent integers.
:: In the latter case, the smaller number is the answer.
::
++ sqrt
|= n=@ud
=/ guess=@ud 1
|-
=/ new-guess (div (add guess (div n guess)) 2)
:: sequence stabilizes
::
?: =(guess new-guess)
guess
:: sequence is trapped in 2-cycle
::
?: =(guess +(new-guess))
new-guess
?: =(new-guess +(guess))
guess
$(guess new-guess)
:: prime-map: (effectively) produces primes less than a given input
::
:: This is the sieve of Eratosthenes to produce primes less than n.
:: I used a map because it had much faster performance than a list.
:: Any key in the map is a non-prime. The value 1 indicates "false."
:: I.e. it's not a prime.
++ prime-map
|= n=@ud
^- (map @ud @ud)
=/ prime-map `(map @ud @ud)`(my ~[[0 1] [1 1]])
:: start sieving with 2
::
=/ sieve 2
|-
:: if sieve is too large to be a factor we're done
::
?: (gte (mul sieve sieve) n)
prime-map
:: if not too large but not prime, move on
::
?: =((~(gut by prime-map) sieve 0) 1)
$(sieve +(sieve))
:: sequence: explanation
::
:: If s is the sieve number, we start sieving multiples
:: of s at s^2 in sequence: s^2, s^2 + s, s^2 + 2s, ...
:: We start at s^2 because any number smaller than s^2
:: has prime factors less than s and would have been
:: eliminated earlier in the sieving process.
::
=/ sequence (mul sieve sieve)
|-
:: done sieving with s once sequence is past n
::
?: (gte sequence n)
^$(sieve +(sieve))
:: if sequence position is known not prime we move on
::
?: =((~(gut by prime-map) sequence 0) 1)
$(sequence (add sequence sieve))
:: otherwise we mark position of sequence as not prime and move on
::
$(prime-map (~(put by prime-map) sequence 1), sequence (add sequence sieve))
--Java
public class RhondaNumbers {
public static void main(String[] args) {
final int limit = 15;
for (int base = 2; base <= 36; ++base) {
if (isPrime(base))
continue;
System.out.printf("First %d Rhonda numbers to base %d:\n", limit, base);
int numbers[] = new int[limit];
for (int n = 1, count = 0; count < limit; ++n) {
if (isRhonda(base, n))
numbers[count++] = n;
}
System.out.printf("In base 10:");
for (int i = 0; i < limit; ++i)
System.out.printf(" %d", numbers[i]);
System.out.printf("\nIn base %d:", base);
for (int i = 0; i < limit; ++i)
System.out.printf(" %s", Integer.toString(numbers[i], base));
System.out.printf("\n\n");
}
}
private static int digitProduct(int base, int n) {
int product = 1;
for (; n != 0; n /= base)
product *= n % base;
return product;
}
private static int primeFactorSum(int n) {
int sum = 0;
for (; (n & 1) == 0; n >>= 1)
sum += 2;
for (int p = 3; p * p <= n; p += 2)
for (; n % p == 0; n /= p)
sum += p;
if (n > 1)
sum += n;
return sum;
}
private static boolean isPrime(int n) {
if (n < 2)
return false;
if (n % 2 == 0)
return n == 2;
if (n % 3 == 0)
return n == 3;
for (int p = 5; p * p <= n; p += 4) {
if (n % p == 0)
return false;
p += 2;
if (n % p == 0)
return false;
}
return true;
}
private static boolean isRhonda(int base, int n) {
return digitProduct(base, n) == base * primeFactorSum(n);
}
}
- Output:
First 15 Rhonda numbers to base 4: In base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713 259753 374782 392121 503773 649902 In base 4: 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221 333122221 1123133332 1133232321 1322333131 2132222232 First 15 Rhonda numbers to base 6: In base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992 41031 42009 60368 65536 67821 In base 6: 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132 513543 522253 1143252 1223224 1241553 First 15 Rhonda numbers to base 8: In base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956 30562 39215 39325 50875 51429 In base 8: 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544 73542 114457 114635 143273 144345 First 15 Rhonda numbers to base 9: In base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857 77142 83334 83694 96448 97944 In base 9: 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376 126733 136273 136723 156264 158316 First 15 Rhonda numbers to base 10: In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662 In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662 First 15 Rhonda numbers to base 12: In base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849 12028 13034 14828 15052 16264 In base 12: 3a8 568 2389 2689 27b6 29b4 4297 4974 5483 6a35 6b64 7662 86b8 8864 94b4 First 15 Rhonda numbers to base 14: In base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945 67525 68904 91245 99603 125543 In base 14: 4279 6b27 76cd ab27 b7c1 1277d 173da 17547 17bc2 19437 1a873 1b17a 25377 28427 33a75 First 15 Rhonda numbers to base 15: In base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758 31150 33004 33550 37925 39483 In base 15: a97 aec 35e8 4a83 5269 5586 5a1c 5e39 735d 91a8 936a 9ba4 9e1a b385 ba73 First 15 Rhonda numbers to base 16: In base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070 31906 32292 34236 34521 36465 In base 16: 3e8 46e 1a78 3e28 4ca8 4e4b 4f83 5d8a 66b8 718e 7ca2 7e24 85bc 86d9 8e71 First 15 Rhonda numbers to base 18: In base 10: 1470 3000 8918 17025 19402 20650 21120 22156 26522 36549 38354 43281 46035 48768 54229 In base 18: 49c 94c 1998 2g9f 35fg 39d4 3b36 3e6g 49f8 64e9 6a6e 77a9 7g19 8696 956d First 15 Rhonda numbers to base 20: In base 10: 1815 11050 15295 21165 22165 30702 34510 34645 42292 44165 52059 53416 65945 78430 80712 In base 20: 4af 17ca 1i4f 2ci5 2f85 3gf2 465a 46c5 55ec 5a85 6a2j 6dag 84h5 9g1a a1fc First 15 Rhonda numbers to base 21: In base 10: 1632 5390 8512 12992 15678 25038 29412 34017 39552 48895 49147 61376 85078 89590 91798 In base 21: 3ef c4e j67 189e 1ebc 2eg6 33ec 3e2i 45e9 55i7 5697 6d3e 93j7 9e34 9j37 First 15 Rhonda numbers to base 22: In base 10: 2695 4128 7865 28800 31710 37030 71875 74306 117760 117895 121626 126002 131427 175065 192753 In base 22: 5cb 8be g5b 2fb2 2lb8 3ab4 6gb1 6lbc b16g b1cj b96a bi78 c7bl g9fb i25b First 15 Rhonda numbers to base 24: In base 10: 2080 2709 3976 5628 5656 7144 8296 9030 10094 17612 20559 24616 26224 29106 31458 In base 24: 3eg 4gl 6lg 9ic 9jg c9g e9g fg6 hce 16dk 1bgf 1ihg 1lcg 22ci 26ei First 15 Rhonda numbers to base 25: In base 10: 6764 9633 13260 22022 53382 57640 66015 69006 97014 140130 142880 144235 159724 162565 165504 In base 25: ake fa8 l5a 1a5m 3aa7 3h5f 45ff 4aa6 655e 8o55 93f5 95ja a5do aa2f aek4 First 15 Rhonda numbers to base 26: In base 10: 7788 9322 9374 11160 22165 27885 34905 44785 47385 49257 62517 72709 74217 108745 132302 In base 26: bde dke dme gd6 16kd 1f6d 1pgd 2e6d 2i2d 2kmd 3ecd 43ed 45kd 64md 7die First 15 Rhonda numbers to base 27: In base 10: 4797 11844 12078 13200 14841 17750 24320 26883 27477 46455 52750 58581 61009 61446 61500 In base 27: 6fi g6i gf9 i2o k9i o9b 169k 19ni 1aii 29jf 2i9j 2q9i 32ig 337l 339l First 15 Rhonda numbers to base 28: In base 10: 3094 5808 5832 7462 11160 13671 27270 28194 28638 39375 39550 49500 50862 52338 52938 In base 28: 3qe 7bc 7c8 9ee e6g hc7 16lq 17qq 18em 1m67 1mce 273o 28oe 2al6 2bei First 15 Rhonda numbers to base 30: In base 10: 3024 3168 5115 5346 5950 6762 7750 7956 8470 9476 9576 9849 10360 11495 13035 In base 30: 3ao 3fi 5kf 5s6 6ia 7fc 8ia 8p6 9ca afq aj6 as9 bfa cn5 eef First 15 Rhonda numbers to base 32: In base 10: 1944 3600 13520 15876 16732 16849 25410 25752 28951 47472 49610 50968 61596 64904 74005 In base 32: 1so 3gg d6g fg4 gas geh oq2 p4o s8n 1ebg 1gea 1hoo 1s4s 1vc8 288l First 15 Rhonda numbers to base 33: In base 10: 756 7040 7568 13826 24930 30613 59345 63555 64372 131427 227840 264044 313709 336385 344858 In base 33: mu 6fb 6vb cmw mtf s3m 1lgb 1pbu 1q3m 3lml 6b78 7bfb 8o2b 9btg 9jm8 First 15 Rhonda numbers to base 34: In base 10: 5661 14161 15620 16473 22185 37145 125579 134692 135405 138472 140369 177086 250665 255552 295614 In base 34: 4uh c8h dhe e8h j6h w4h 36lh 3ehi 3f4h 3hqo 3jeh 4h6e 6csh 6h28 7hoi First 15 Rhonda numbers to base 35: In base 10: 8232 9476 9633 18634 30954 41905 52215 52440 56889 61992 62146 66339 98260 102180 103305 In base 35: 6p7 7pq 7u8 f7e p9e y7a 17lu 17sa 1bfe 1fl7 1fpl 1j5e 2a7f 2def 2ebk First 15 Rhonda numbers to base 36: In base 10: 1000 4800 5670 8190 10998 12412 13300 15750 16821 23016 51612 52734 67744 70929 75030 In base 36: rs 3pc 4di 6bi 8hi 9ks a9g c5i cz9 hrc 13to 14ou 1g9s 1iq9 1lw6
jq
Works with jq and gojq, that is, the C and Go implementations of jq.
Adapted from Wren
Generic stream-oriented utility functions
def prod(s): reduce s as $_ (1; . * $_);
def sigma(s): reduce s as $_ (0; . + $_);
# If s is a stream of JSON entities that does not include null, butlast(s) emits all but the last.
def butlast(s):
label $out
| foreach (s,null) as $x ({};
if $x == null then break $out else .emit = .prev | .prev = $x end)
| select(.emit).emit;
def multiple(s):
first(foreach s as $x (0; .+1; select(. > 1))) // false;
# Output: a stream of the prime factors of the input
# e.g.
# 2 | factors #=> 2
# 24 | factors #=> 2 2 2 3
def factors:
. as $in
| [2, $in, false]
| recurse(
. as [$p, $q, $valid, $s]
| if $q == 1 then empty
elif $q % $p == 0 then [$p, $q/$p, true]
elif $p == 2 then [3, $q, false, $s]
else ($s // ($q | sqrt)) as $s
| if $p + 2 <= $s then [$p + 2, $q, false, $s]
else [$q, 1, true]
end
end )
| if .[2] then .[0] else empty end ;Other generic functions
def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;
def is_prime:
multiple(factors) | not;
def tobase($b):
def digit: "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"[.:.+1];
def mod: . % $b;
def div: ((. - mod) / $b);
def digits: recurse( select(. > 0) | div) | mod ;
# For jq it would be wise to protect against `infinite` as input, but using `isinfinite` confuses gojq
select( (tostring|test("^[0-9]+$")) and 2 <= $b and $b <= 36)
| if . == 0 then "0"
else [digits | digit] | reverse[1:] | add
end;
# emit the decimal values of the "digits"
def digits($b):
def mod: . % $b;
def div: ((. - mod) / $b);
butlast(recurse( select(. > 0) | div) | mod) ;Rhonda numbers
# Emit a stream of Rhonda numbers in the given base
def rhondas($b):
range(1; infinite) as $n
| ($n | [digits($b)]) as $digits
| select($digits|index(0)|not)
| select(($b != 10) or (($digits|index(5)) and ($digits | any(. % 2 == 0))))
| select(prod($digits[]) == ($b * sigma($n | factors)))
| $n ;The task
def task($count):
range (2; 37) as $b
| select( $b | is_prime | not)
| [ limit($count; rhondas($b)) ]
| select(length > 0)
|"First \($count) Rhonda numbers in base \($b):",
( (map(tostring)) as $rhonda2
| (map(tobase($b))) as $rhonda3
| (($rhonda2|map(length)) | max) as $maxLen2
| (($rhonda3|map(length)) | max) as $maxLen3
| ( ([$maxLen2, $maxLen3]|max) + 1) as $maxLen
| "In base 10: \($rhonda2 | map(lpad($maxLen)) | join(" ") )",
"In base \($b|lpad(2)): \($rhonda3 | map(lpad($maxLen)) | join(" ") )",
"") ;
task(10)- Output:
First 10 Rhonda numbers in base 4: In base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713 In base 4: 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221 First 10 Rhonda numbers in base 6: In base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992 In base 6: 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132 First 10 Rhonda numbers in base 8: In base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956 In base 8: 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544 First 10 Rhonda numbers in base 9: In base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857 In base 9: 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376 First 10 Rhonda numbers in base 10: In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 First 10 Rhonda numbers in base 12: In base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849 In base 12: 3A8 568 2389 2689 27B6 29B4 4297 4974 5483 6A35 First 10 Rhonda numbers in base 14: In base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945 In base 14: 4279 6B27 76CD AB27 B7C1 1277D 173DA 17547 17BC2 19437 First 10 Rhonda numbers in base 15: In base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758 In base 15: A97 AEC 35E8 4A83 5269 5586 5A1C 5E39 735D 91A8 First 10 Rhonda numbers in base 16: In base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070 In base 16: 3E8 46E 1A78 3E28 4CA8 4E4B 4F83 5D8A 66B8 718E First 10 Rhonda numbers in base 18: In base 10: 1470 3000 8918 17025 19402 20650 21120 22156 26522 36549 In base 18: 49C 94C 1998 2G9F 35FG 39D4 3B36 3E6G 49F8 64E9 First 10 Rhonda numbers in base 20: In base 10: 1815 11050 15295 21165 22165 30702 34510 34645 42292 44165 In base 20: 4AF 17CA 1I4F 2CI5 2F85 3GF2 465A 46C5 55EC 5A85 First 10 Rhonda numbers in base 21: In base 10: 1632 5390 8512 12992 15678 25038 29412 34017 39552 48895 In base 21: 3EF C4E J67 189E 1EBC 2EG6 33EC 3E2I 45E9 55I7 First 10 Rhonda numbers in base 22: In base 10: 2695 4128 7865 28800 31710 37030 71875 74306 117760 117895 In base 22: 5CB 8BE G5B 2FB2 2LB8 3AB4 6GB1 6LBC B16G B1CJ First 10 Rhonda numbers in base 24: In base 10: 2080 2709 3976 5628 5656 7144 8296 9030 10094 17612 In base 24: 3EG 4GL 6LG 9IC 9JG C9G E9G FG6 HCE 16DK First 10 Rhonda numbers in base 25: In base 10: 6764 9633 13260 22022 53382 57640 66015 69006 97014 140130 In base 25: AKE FA8 L5A 1A5M 3AA7 3H5F 45FF 4AA6 655E 8O55 First 10 Rhonda numbers in base 26: In base 10: 7788 9322 9374 11160 22165 27885 34905 44785 47385 49257 In base 26: BDE DKE DME GD6 16KD 1F6D 1PGD 2E6D 2I2D 2KMD First 10 Rhonda numbers in base 27: In base 10: 4797 11844 12078 13200 14841 17750 24320 26883 27477 46455 In base 27: 6FI G6I GF9 I2O K9I O9B 169K 19NI 1AII 29JF First 10 Rhonda numbers in base 28: In base 10: 3094 5808 5832 7462 11160 13671 27270 28194 28638 39375 In base 28: 3QE 7BC 7C8 9EE E6G HC7 16LQ 17QQ 18EM 1M67 First 10 Rhonda numbers in base 30: In base 10: 3024 3168 5115 5346 5950 6762 7750 7956 8470 9476 In base 30: 3AO 3FI 5KF 5S6 6IA 7FC 8IA 8P6 9CA AFQ First 10 Rhonda numbers in base 32: In base 10: 1944 3600 13520 15876 16732 16849 25410 25752 28951 47472 In base 32: 1SO 3GG D6G FG4 GAS GEH OQ2 P4O S8N 1EBG First 10 Rhonda numbers in base 33: In base 10: 756 7040 7568 13826 24930 30613 59345 63555 64372 131427 In base 33: MU 6FB 6VB CMW MTF S3M 1LGB 1PBU 1Q3M 3LML First 10 Rhonda numbers in base 34: In base 10: 5661 14161 15620 16473 22185 37145 125579 134692 135405 138472 In base 34: 4UH C8H DHE E8H J6H W4H 36LH 3EHI 3F4H 3HQO First 10 Rhonda numbers in base 35: In base 10: 8232 9476 9633 18634 30954 41905 52215 52440 56889 61992 In base 35: 6P7 7PQ 7U8 F7E P9E Y7A 17LU 17SA 1BFE 1FL7 First 10 Rhonda numbers in base 36: In base 10: 1000 4800 5670 8190 10998 12412 13300 15750 16821 23016 In base 36: RS 3PC 4DI 6BI 8HI 9KS A9G C5I CZ9 HRC
Julia
using Primes
isRhonda(n, b) = prod(digits(n, base=b)) == b * sum([prod(pair) for pair in factor(n).pe])
function displayrhondas(low, high, nshow)
for b in filter(!isprime, low:high)
n, rhondas = 1, Int[]
while length(rhondas) < nshow
isRhonda(n, b) && push!(rhondas, n)
n += 1
end
println("First $nshow Rhondas in base $b:")
println("In base 10: ", rhondas)
println("In base $b: ", replace(string([string(i, base=b) for i in rhondas]), "\"" => ""), "\n")
end
end
displayrhondas(2, 16, 15)
- Output:
First 15 Rhondas in base 4: In base 10: [10206, 11935, 12150, 16031, 45030, 94185, 113022, 114415, 191149, 244713, 259753, 374782, 392121, 503773, 649902] In base 4: [2133132, 2322133, 2331312, 3322133, 22333212, 112333221, 123211332, 123323233, 232222231, 323233221, 333122221, 1123133332, 1133232321, 1322333131, 2132222232] First 15 Rhondas in base 6: In base 10: [855, 1029, 3813, 5577, 7040, 7304, 15104, 19136, 35350, 36992, 41031, 42009, 60368, 65536, 67821] In base 6: [3543, 4433, 25353, 41453, 52332, 53452, 153532, 224332, 431354, 443132, 513543, 522253, 1143252, 1223224, 1241553] First 15 Rhondas in base 8: In base 10: [1836, 6318, 6622, 10530, 14500, 14739, 17655, 18550, 25398, 25956, 30562, 39215, 39325, 50875, 51429] In base 8: [3454, 14256, 14736, 24442, 34244, 34623, 42367, 44166, 61466, 62544, 73542, 114457, 114635, 143273, 144345] First 15 Rhondas in base 9: In base 10: [15540, 21054, 25331, 44360, 44660, 44733, 47652, 50560, 54944, 76857, 77142, 83334, 83694, 96448, 97944] In base 9: [23276, 31783, 37665, 66758, 67232, 67323, 72326, 76317, 83328, 126376, 126733, 136273, 136723, 156264, 158316] First 15 Rhondas in base 10: In base 10: [1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985, 15625, 15698, 19435, 25284, 25662] In base 10: [1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985, 15625, 15698, 19435, 25284, 25662] First 15 Rhondas in base 12: In base 10: [560, 800, 3993, 4425, 4602, 4888, 7315, 8296, 9315, 11849, 12028, 13034, 14828, 15052, 16264] In base 12: [3a8, 568, 2389, 2689, 27b6, 29b4, 4297, 4974, 5483, 6a35, 6b64, 7662, 86b8, 8864, 94b4] First 15 Rhondas in base 14: In base 10: [11475, 18655, 20565, 29631, 31725, 45387, 58404, 58667, 59950, 63945, 67525, 68904, 91245, 99603, 125543] In base 14: [4279, 6b27, 76cd, ab27, b7c1, 1277d, 173da, 17547, 17bc2, 19437, 1a873, 1b17a, 25377, 28427, 33a75] First 15 Rhondas in base 15: In base 10: [2392, 2472, 11468, 15873, 17424, 18126, 19152, 20079, 24388, 30758, 31150, 33004, 33550, 37925, 39483] In base 15: [a97, aec, 35e8, 4a83, 5269, 5586, 5a1c, 5e39, 735d, 91a8, 936a, 9ba4, 9e1a, b385, ba73] First 15 Rhondas in base 16: In base 10: [1000, 1134, 6776, 15912, 19624, 20043, 20355, 23946, 26296, 29070, 31906, 32292, 34236, 34521, 36465] In base 16: [3e8, 46e, 1a78, 3e28, 4ca8, 4e4b, 4f83, 5d8a, 66b8, 718e, 7ca2, 7e24, 85bc, 86d9, 8e71]
Mathematica /Wolfram Language
ClearAll[RhondaNumberQ]
RhondaNumberQ[b_Integer][n_Integer] := Module[{l, r},
l = Times @@ IntegerDigits[n, b];
r = Total[Catenate[ConstantArray @@@ FactorInteger[n]]];
l == b r
]
bases = Select[Range[2, 36], PrimeQ/*Not];
Do[
Print["base ", b, ":", Take[Select[Range[700000], RhondaNumberQ[b]], UpTo[15]]];
,
{b, bases}
]
- Output:
base 4:{10206,11935,12150,16031,45030,94185,113022,114415,191149,244713,259753,374782,392121,503773,649902}
base 6:{855,1029,3813,5577,7040,7304,15104,19136,35350,36992,41031,42009,60368,65536,67821}
base 8:{1836,6318,6622,10530,14500,14739,17655,18550,25398,25956,30562,39215,39325,50875,51429}
base 9:{15540,21054,25331,44360,44660,44733,47652,50560,54944,76857,77142,83334,83694,96448,97944}
base 10:{1568,2835,4752,5265,5439,5664,5824,5832,8526,12985,15625,15698,19435,25284,25662}
base 12:{560,800,3993,4425,4602,4888,7315,8296,9315,11849,12028,13034,14828,15052,16264}
base 14:{11475,18655,20565,29631,31725,45387,58404,58667,59950,63945,67525,68904,91245,99603,125543}
base 15:{2392,2472,11468,15873,17424,18126,19152,20079,24388,30758,31150,33004,33550,37925,39483}
base 16:{1000,1134,6776,15912,19624,20043,20355,23946,26296,29070,31906,32292,34236,34521,36465}
base 18:{1470,3000,8918,17025,19402,20650,21120,22156,26522,36549,38354,43281,46035,48768,54229}
base 20:{1815,11050,15295,21165,22165,30702,34510,34645,42292,44165,52059,53416,65945,78430,80712}
base 21:{1632,5390,8512,12992,15678,25038,29412,34017,39552,48895,49147,61376,85078,89590,91798}
base 22:{2695,4128,7865,28800,31710,37030,71875,74306,117760,117895,121626,126002,131427,175065,192753}
base 24:{2080,2709,3976,5628,5656,7144,8296,9030,10094,17612,20559,24616,26224,29106,31458}
base 25:{6764,9633,13260,22022,53382,57640,66015,69006,97014,140130,142880,144235,159724,162565,165504}
base 26:{7788,9322,9374,11160,22165,27885,34905,44785,47385,49257,62517,72709,74217,108745,132302}
base 27:{4797,11844,12078,13200,14841,17750,24320,26883,27477,46455,52750,58581,61009,61446,61500}
base 28:{3094,5808,5832,7462,11160,13671,27270,28194,28638,39375,39550,49500,50862,52338,52938}
base 30:{3024,3168,5115,5346,5950,6762,7750,7956,8470,9476,9576,9849,10360,11495,13035}
base 32:{1944,3600,13520,15876,16732,16849,25410,25752,28951,47472,49610,50968,61596,64904,74005}
base 33:{756,7040,7568,13826,24930,30613,59345,63555,64372,131427,227840,264044,313709,336385,344858}
base 34:{5661,14161,15620,16473,22185,37145,125579,134692,135405,138472,140369,177086,250665,255552,295614}
base 35:{8232,9476,9633,18634,30954,41905,52215,52440,56889,61992,62146,66339,98260,102180,103305}
base 36:{1000,4800,5670,8190,10998,12412,13300,15750,16821,23016,51612,52734,67744,70929,75030}
Nim
import std/[sequtils, strformat, strutils]
type Base = 2..36
template isEven(n: int): bool = (n and 1) == 0
func isPrime(n: Natural): bool =
## Return true if "n" is prime.
if n < 2: return false
if n.isEven: return n == 2
if n mod 3 == 0: return n == 3
var d = 5
while d * d <= n:
if n mod d == 0: return false
inc d, 2
return true
func digitProduct(n: Positive; base: Base): int =
## Return the product of digits of "n" in given base.
var n = n.Natural
result = 1
while n != 0:
result *= n mod base
n = n div base
func primeFactorSum(n: Positive): int =
## Return the sum of prime factors of "n".
var n = n.Natural
while n.isEven:
inc result, 2
n = n shr 1
var d = 3
while d * d <= n:
while n mod d == 0:
inc result, d
n = n div d
inc d, 2
if n > 1: inc result, n
func isRhondaNumber(n: Positive; base: Base): bool =
## Return true if "n" is a Rhonda number to given base.
n.digitProduct(base) == base * n.primeFactorSum
const Digits = toSeq('0'..'9') & toSeq('a'..'z')
func toBase(n: Positive; base: Base): string =
## Return the string representation of "n" in given base.
var n = n.Natural
while true:
result.add Digits[n mod base]
n = n div base
if n == 0: break
# Reverse the digits.
for i in 1..(result.len shr 1):
swap result[i - 1], result[^i]
const N = 10
for base in 2..36:
if base.isPrime: continue
echo &"First {N} Rhonda numbers to base {base}:"
var rhondaList: seq[Positive]
var n = 1
var count = 0
while count < N:
if n.isRhondaNumber(base):
rhondaList.add n
inc count
inc n
echo "In base 10: ", rhondaList.join(" ")
echo &"In base {base}: ", rhondaList.mapIt(it.toBase(base)).join(" ")
echo()
- Output:
First 10 Rhonda numbers to base 4: In base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713 In base 4: 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221 First 10 Rhonda numbers to base 6: In base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992 In base 6: 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132 First 10 Rhonda numbers to base 8: In base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956 In base 8: 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544 First 10 Rhonda numbers to base 9: In base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857 In base 9: 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376 First 10 Rhonda numbers to base 10: In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 First 10 Rhonda numbers to base 12: In base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849 In base 12: 3a8 568 2389 2689 27b6 29b4 4297 4974 5483 6a35 First 10 Rhonda numbers to base 14: In base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945 In base 14: 4279 6b27 76cd ab27 b7c1 1277d 173da 17547 17bc2 19437 First 10 Rhonda numbers to base 15: In base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758 In base 15: a97 aec 35e8 4a83 5269 5586 5a1c 5e39 735d 91a8 First 10 Rhonda numbers to base 16: In base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070 In base 16: 3e8 46e 1a78 3e28 4ca8 4e4b 4f83 5d8a 66b8 718e First 10 Rhonda numbers to base 18: In base 10: 1470 3000 8918 17025 19402 20650 21120 22156 26522 36549 In base 18: 49c 94c 1998 2g9f 35fg 39d4 3b36 3e6g 49f8 64e9 First 10 Rhonda numbers to base 20: In base 10: 1815 11050 15295 21165 22165 30702 34510 34645 42292 44165 In base 20: 4af 17ca 1i4f 2ci5 2f85 3gf2 465a 46c5 55ec 5a85 First 10 Rhonda numbers to base 21: In base 10: 1632 5390 8512 12992 15678 25038 29412 34017 39552 48895 In base 21: 3ef c4e j67 189e 1ebc 2eg6 33ec 3e2i 45e9 55i7 First 10 Rhonda numbers to base 22: In base 10: 2695 4128 7865 28800 31710 37030 71875 74306 117760 117895 In base 22: 5cb 8be g5b 2fb2 2lb8 3ab4 6gb1 6lbc b16g b1cj First 10 Rhonda numbers to base 24: In base 10: 2080 2709 3976 5628 5656 7144 8296 9030 10094 17612 In base 24: 3eg 4gl 6lg 9ic 9jg c9g e9g fg6 hce 16dk First 10 Rhonda numbers to base 25: In base 10: 6764 9633 13260 22022 53382 57640 66015 69006 97014 140130 In base 25: ake fa8 l5a 1a5m 3aa7 3h5f 45ff 4aa6 655e 8o55 First 10 Rhonda numbers to base 26: In base 10: 7788 9322 9374 11160 22165 27885 34905 44785 47385 49257 In base 26: bde dke dme gd6 16kd 1f6d 1pgd 2e6d 2i2d 2kmd First 10 Rhonda numbers to base 27: In base 10: 4797 11844 12078 13200 14841 17750 24320 26883 27477 46455 In base 27: 6fi g6i gf9 i2o k9i o9b 169k 19ni 1aii 29jf First 10 Rhonda numbers to base 28: In base 10: 3094 5808 5832 7462 11160 13671 27270 28194 28638 39375 In base 28: 3qe 7bc 7c8 9ee e6g hc7 16lq 17qq 18em 1m67 First 10 Rhonda numbers to base 30: In base 10: 3024 3168 5115 5346 5950 6762 7750 7956 8470 9476 In base 30: 3ao 3fi 5kf 5s6 6ia 7fc 8ia 8p6 9ca afq First 10 Rhonda numbers to base 32: In base 10: 1944 3600 13520 15876 16732 16849 25410 25752 28951 47472 In base 32: 1so 3gg d6g fg4 gas geh oq2 p4o s8n 1ebg First 10 Rhonda numbers to base 33: In base 10: 756 7040 7568 13826 24930 30613 59345 63555 64372 131427 In base 33: mu 6fb 6vb cmw mtf s3m 1lgb 1pbu 1q3m 3lml First 10 Rhonda numbers to base 34: In base 10: 5661 14161 15620 16473 22185 37145 125579 134692 135405 138472 In base 34: 4uh c8h dhe e8h j6h w4h 36lh 3ehi 3f4h 3hqo First 10 Rhonda numbers to base 35: In base 10: 8232 9476 9633 18634 30954 41905 52215 52440 56889 61992 In base 35: 6p7 7pq 7u8 f7e p9e y7a 17lu 17sa 1bfe 1fl7 First 10 Rhonda numbers to base 36: In base 10: 1000 4800 5670 8190 10998 12412 13300 15750 16821 23016 In base 36: rs 3pc 4di 6bi 8hi 9ks a9g c5i cz9 hrc
PARI/GP
isRhonda(n, b) =
{
local(mydigits, product, mysum, factors, pairProduct);
mydigits = digits(n, b);
product = vecprod(mydigits);
factors = factor(n);
mysum= 0;
for(i = 1, matsize(factors)[1],
pairProduct = factors[i, 1] * factors[i, 2];
mysum += pairProduct;
);
product == b * mysum;
}
displayrhondas(low, high, nshow) =
{
local(b, n, rhondas, count, basebRhondas);
for(b = low, high,
if(isprime(b), next);
n = 1; rhondas = [];
count = 0;
while(count < nshow,
if(isRhonda(n, b),
rhondas = concat(rhondas, n);
count++;
);
n++;
);
print("First " nshow " Rhondas in base " b ":");
print("In base 10: " rhondas);
basebRhondas = vector(#rhondas, i, (digits(rhondas[i], b)));
print("In base " b ": " basebRhondas);
print("\n");
);
}
displayrhondas(2, 16, 15);- Output:
First 15 Rhondas in base 4: In base 10: [10206, 11935, 12150, 16031, 45030, 94185, 113022, 114415, 191149, 244713, 259753, 374782, 392121, 503773, 649902] In base 4: [[2, 1, 3, 3, 1, 3, 2], [2, 3, 2, 2, 1, 3, 3], [2, 3, 3, 1, 3, 1, 2], [3, 3, 2, 2, 1, 3, 3], [2, 2, 3, 3, 3, 2, 1, 2], [1, 1, 2, 3, 3, 3, 2, 2, 1], [1, 2, 3, 2, 1, 1, 3, 3, 2], [1, 2, 3, 3, 2, 3, 2, 3, 3], [2, 3, 2, 2, 2, 2, 2, 3, 1], [3, 2, 3, 2, 3, 3, 2, 2, 1], [3, 3, 3, 1, 2, 2, 2, 2, 1], [1, 1, 2, 3, 1, 3, 3, 3, 3, 2], [1, 1, 3, 3, 2, 3, 2, 3, 2, 1], [1, 3, 2, 2, 3, 3, 3, 1, 3, 1], [2, 1, 3, 2, 2, 2, 2, 2, 3, 2]] First 15 Rhondas in base 6: In base 10: [855, 1029, 3813, 5577, 7040, 7304, 15104, 19136, 35350, 36992, 41031, 42009, 60368, 65536, 67821] In base 6: [[3, 5, 4, 3], [4, 4, 3, 3], [2, 5, 3, 5, 3], [4, 1, 4, 5, 3], [5, 2, 3, 3, 2], [5, 3, 4, 5, 2], [1, 5, 3, 5, 3, 2], [2, 2, 4, 3, 3, 2], [4, 3, 1, 3, 5, 4], [4, 4, 3, 1, 3, 2], [5, 1, 3, 5, 4, 3], [5, 2, 2, 2, 5, 3], [1, 1, 4, 3, 2, 5, 2], [1, 2, 2, 3, 2, 2, 4], [1, 2, 4, 1, 5, 5, 3]] First 15 Rhondas in base 8: In base 10: [1836, 6318, 6622, 10530, 14500, 14739, 17655, 18550, 25398, 25956, 30562, 39215, 39325, 50875, 51429] In base 8: [[3, 4, 5, 4], [1, 4, 2, 5, 6], [1, 4, 7, 3, 6], [2, 4, 4, 4, 2], [3, 4, 2, 4, 4], [3, 4, 6, 2, 3], [4, 2, 3, 6, 7], [4, 4, 1, 6, 6], [6, 1, 4, 6, 6], [6, 2, 5, 4, 4], [7, 3, 5, 4, 2], [1, 1, 4, 4, 5, 7], [1, 1, 4, 6, 3, 5], [1, 4, 3, 2, 7, 3], [1, 4, 4, 3, 4, 5]] First 15 Rhondas in base 9: In base 10: [15540, 21054, 25331, 44360, 44660, 44733, 47652, 50560, 54944, 76857, 77142, 83334, 83694, 96448, 97944] In base 9: [[2, 3, 2, 7, 6], [3, 1, 7, 8, 3], [3, 7, 6, 6, 5], [6, 6, 7, 5, 8], [6, 7, 2, 3, 2], [6, 7, 3, 2, 3], [7, 2, 3, 2, 6], [7, 6, 3, 1, 7], [8, 3, 3, 2, 8], [1, 2, 6, 3, 7, 6], [1, 2, 6, 7, 3, 3], [1, 3, 6, 2, 7, 3], [1, 3, 6, 7, 2, 3], [1, 5, 6, 2, 6, 4], [1, 5, 8, 3, 1, 6]] First 15 Rhondas in base 10: In base 10: [1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985, 15625, 15698, 19435, 25284, 25662] In base 10: [[1, 5, 6, 8], [2, 8, 3, 5], [4, 7, 5, 2], [5, 2, 6, 5], [5, 4, 3, 9], [5, 6, 6, 4], [5, 8, 2, 4], [5, 8, 3, 2], [8, 5, 2, 6], [1, 2, 9, 8, 5], [1, 5, 6, 2, 5], [1, 5, 6, 9, 8], [1, 9, 4, 3, 5], [2, 5, 2, 8, 4], [2, 5, 6, 6, 2]] First 15 Rhondas in base 12: In base 10: [560, 800, 3993, 4425, 4602, 4888, 7315, 8296, 9315, 11849, 12028, 13034, 14828, 15052, 16264] In base 12: [[3, 10, 8], [5, 6, 8], [2, 3, 8, 9], [2, 6, 8, 9], [2, 7, 11, 6], [2, 9, 11, 4], [4, 2, 9, 7], [4, 9, 7, 4], [5, 4, 8, 3], [6, 10, 3, 5], [6, 11, 6, 4], [7, 6, 6, 2], [8, 6, 11, 8], [8, 8, 6, 4], [9, 4, 11, 4]] First 15 Rhondas in base 14: In base 10: [11475, 18655, 20565, 29631, 31725, 45387, 58404, 58667, 59950, 63945, 67525, 68904, 91245, 99603, 125543] In base 14: [[4, 2, 7, 9], [6, 11, 2, 7], [7, 6, 12, 13], [10, 11, 2, 7], [11, 7, 12, 1], [1, 2, 7, 7, 13], [1, 7, 3, 13, 10], [1, 7, 5, 4, 7], [1, 7, 11, 12, 2], [1, 9, 4, 3, 7], [1, 10, 8, 7, 3], [1, 11, 1, 7, 10], [2, 5, 3, 7, 7], [2, 8, 4, 2, 7], [3, 3, 10, 7, 5]] First 15 Rhondas in base 15: In base 10: [2392, 2472, 11468, 15873, 17424, 18126, 19152, 20079, 24388, 30758, 31150, 33004, 33550, 37925, 39483] In base 15: [[10, 9, 7], [10, 14, 12], [3, 5, 14, 8], [4, 10, 8, 3], [5, 2, 6, 9], [5, 5, 8, 6], [5, 10, 1, 12], [5, 14, 3, 9], [7, 3, 5, 13], [9, 1, 10, 8], [9, 3, 6, 10], [9, 11, 10, 4], [9, 14, 1, 10], [11, 3, 8, 5], [11, 10, 7, 3]] First 15 Rhondas in base 16: In base 10: [1000, 1134, 6776, 15912, 19624, 20043, 20355, 23946, 26296, 29070, 31906, 32292, 34236, 34521, 36465] In base 16: [[3, 14, 8], [4, 6, 14], [1, 10, 7, 8], [3, 14, 2, 8], [4, 12, 10, 8], [4, 14, 4, 11], [4, 15, 8, 3], [5, 13, 8, 10], [6, 6, 11, 8], [7, 1, 8, 14], [7, 12, 10, 2], [7, 14, 2, 4], [8, 5, 11, 12], [8, 6, 13, 9], [8, 14, 7, 1]]
Perl
use strict;
use warnings;
use feature 'say';
use ntheory qw<is_prime factor vecsum vecprod todigitstring todigits>;
sub rhonda {
my($b, $cnt) = @_;
my(@r,$n);
while (++$n) {
push @r, $n if ($b * vecsum factor($n)) == vecprod todigits($n,$b);
return @r if $cnt == @r;
}
}
for my $b (grep { ! is_prime $_ } 2..36) {
my @Rb = map { todigitstring($_,$b) } my @R = rhonda($b, 15);
say <<~EOT;
First 15 Rhonda numbers to base $b:
In base $b: @Rb
In base 10: @R
EOT
}
- Output:
First 15 Rhonda numbers to base 4: In base 4: 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221 333122221 1123133332 1133232321 1322333131 2132222232 In base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713 259753 374782 392121 503773 649902 First 15 Rhonda numbers to base 6: In base 6: 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132 513543 522253 1143252 1223224 1241553 In base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992 41031 42009 60368 65536 67821 First 15 Rhonda numbers to base 8: In base 8: 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544 73542 114457 114635 143273 144345 In base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956 30562 39215 39325 50875 51429 First 15 Rhonda numbers to base 9: In base 9: 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376 126733 136273 136723 156264 158316 In base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857 77142 83334 83694 96448 97944 First 15 Rhonda numbers to base 10: In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662 In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662 First 15 Rhonda numbers to base 12: In base 12: 3a8 568 2389 2689 27b6 29b4 4297 4974 5483 6a35 6b64 7662 86b8 8864 94b4 In base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849 12028 13034 14828 15052 16264 First 15 Rhonda numbers to base 14: In base 14: 4279 6b27 76cd ab27 b7c1 1277d 173da 17547 17bc2 19437 1a873 1b17a 25377 28427 33a75 In base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945 67525 68904 91245 99603 125543 First 15 Rhonda numbers to base 15: In base 15: a97 aec 35e8 4a83 5269 5586 5a1c 5e39 735d 91a8 936a 9ba4 9e1a b385 ba73 In base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758 31150 33004 33550 37925 39483 First 15 Rhonda numbers to base 16: In base 16: 3e8 46e 1a78 3e28 4ca8 4e4b 4f83 5d8a 66b8 718e 7ca2 7e24 85bc 86d9 8e71 In base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070 31906 32292 34236 34521 36465 First 15 Rhonda numbers to base 18: In base 18: 49c 94c 1998 2g9f 35fg 39d4 3b36 3e6g 49f8 64e9 6a6e 77a9 7g19 8696 956d In base 10: 1470 3000 8918 17025 19402 20650 21120 22156 26522 36549 38354 43281 46035 48768 54229 First 15 Rhonda numbers to base 20: In base 20: 4af 17ca 1i4f 2ci5 2f85 3gf2 465a 46c5 55ec 5a85 6a2j 6dag 84h5 9g1a a1fc In base 10: 1815 11050 15295 21165 22165 30702 34510 34645 42292 44165 52059 53416 65945 78430 80712 First 15 Rhonda numbers to base 21: In base 21: 3ef c4e j67 189e 1ebc 2eg6 33ec 3e2i 45e9 55i7 5697 6d3e 93j7 9e34 9j37 In base 10: 1632 5390 8512 12992 15678 25038 29412 34017 39552 48895 49147 61376 85078 89590 91798 First 15 Rhonda numbers to base 22: In base 22: 5cb 8be g5b 2fb2 2lb8 3ab4 6gb1 6lbc b16g b1cj b96a bi78 c7bl g9fb i25b In base 10: 2695 4128 7865 28800 31710 37030 71875 74306 117760 117895 121626 126002 131427 175065 192753 First 15 Rhonda numbers to base 24: In base 24: 3eg 4gl 6lg 9ic 9jg c9g e9g fg6 hce 16dk 1bgf 1ihg 1lcg 22ci 26ei In base 10: 2080 2709 3976 5628 5656 7144 8296 9030 10094 17612 20559 24616 26224 29106 31458 First 15 Rhonda numbers to base 25: In base 25: ake fa8 l5a 1a5m 3aa7 3h5f 45ff 4aa6 655e 8o55 93f5 95ja a5do aa2f aek4 In base 10: 6764 9633 13260 22022 53382 57640 66015 69006 97014 140130 142880 144235 159724 162565 165504 First 15 Rhonda numbers to base 26: In base 26: bde dke dme gd6 16kd 1f6d 1pgd 2e6d 2i2d 2kmd 3ecd 43ed 45kd 64md 7die In base 10: 7788 9322 9374 11160 22165 27885 34905 44785 47385 49257 62517 72709 74217 108745 132302 First 15 Rhonda numbers to base 27: In base 27: 6fi g6i gf9 i2o k9i o9b 169k 19ni 1aii 29jf 2i9j 2q9i 32ig 337l 339l In base 10: 4797 11844 12078 13200 14841 17750 24320 26883 27477 46455 52750 58581 61009 61446 61500 First 15 Rhonda numbers to base 28: In base 28: 3qe 7bc 7c8 9ee e6g hc7 16lq 17qq 18em 1m67 1mce 273o 28oe 2al6 2bei In base 10: 3094 5808 5832 7462 11160 13671 27270 28194 28638 39375 39550 49500 50862 52338 52938 First 15 Rhonda numbers to base 30: In base 30: 3ao 3fi 5kf 5s6 6ia 7fc 8ia 8p6 9ca afq aj6 as9 bfa cn5 eef In base 10: 3024 3168 5115 5346 5950 6762 7750 7956 8470 9476 9576 9849 10360 11495 13035 First 15 Rhonda numbers to base 32: In base 32: 1so 3gg d6g fg4 gas geh oq2 p4o s8n 1ebg 1gea 1hoo 1s4s 1vc8 288l In base 10: 1944 3600 13520 15876 16732 16849 25410 25752 28951 47472 49610 50968 61596 64904 74005 First 15 Rhonda numbers to base 33: In base 33: mu 6fb 6vb cmw mtf s3m 1lgb 1pbu 1q3m 3lml 6b78 7bfb 8o2b 9btg 9jm8 In base 10: 756 7040 7568 13826 24930 30613 59345 63555 64372 131427 227840 264044 313709 336385 344858 First 15 Rhonda numbers to base 34: In base 34: 4uh c8h dhe e8h j6h w4h 36lh 3ehi 3f4h 3hqo 3jeh 4h6e 6csh 6h28 7hoi In base 10: 5661 14161 15620 16473 22185 37145 125579 134692 135405 138472 140369 177086 250665 255552 295614 First 15 Rhonda numbers to base 35: In base 35: 6p7 7pq 7u8 f7e p9e y7a 17lu 17sa 1bfe 1fl7 1fpl 1j5e 2a7f 2def 2ebk In base 10: 8232 9476 9633 18634 30954 41905 52215 52440 56889 61992 62146 66339 98260 102180 103305 First 15 Rhonda numbers to base 36: In base 36: rs 3pc 4di 6bi 8hi 9ks a9g c5i cz9 hrc 13to 14ou 1g9s 1iq9 1lw6 In base 10: 1000 4800 5670 8190 10998 12412 13300 15750 16821 23016 51612 52734 67744 70929 75030
Phix
with javascript_semantics constant fmt = """ First 15 Rhonda numbers in base %d: In base 10: %s In base %-2d: %s """ function digit(integer d) return d-iff(d<='9'?'0':'a'-10) end function for base=2 to 36 do if not is_prime(base) then sequence rhondab = {}, -- (base) rhondad = {} -- (decimal) integer n = 1 while length(rhondab)<15 do string digits = sprintf("%a",{{base,n}}) if not find('0',digits) and (base!=10 or (find('5',digits) and sum(apply(digits,even))!=0)) then integer pd = product(apply(digits,digit)), bs = base*sum(prime_factors(n,true,-1)) if pd==bs then string decdig = sprintf("%d",n) integer l = max(length(decdig),length(digits)) rhondab = append(rhondab,pad_head(digits,l)) rhondad = append(rhondad,pad_head(decdig,l)) end if end if n += 1 end while printf(1,fmt,{base,join(rhondad),base,join(rhondab)}) end if end for
- Output:
First 15 Rhonda numbers in base 4: In base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713 259753 374782 392121 503773 649902 In base 4 : 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221 333122221 1123133332 1133232321 1322333131 2132222232 First 15 Rhonda numbers in base 6: In base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992 41031 42009 60368 65536 67821 In base 6 : 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132 513543 522253 1143252 1223224 1241553 First 15 Rhonda numbers in base 8: In base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956 30562 39215 39325 50875 51429 In base 8 : 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544 73542 114457 114635 143273 144345 First 15 Rhonda numbers in base 9: In base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857 77142 83334 83694 96448 97944 In base 9 : 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376 126733 136273 136723 156264 158316 First 15 Rhonda numbers in base 10: In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662 In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662 First 15 Rhonda numbers in base 12: In base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849 12028 13034 14828 15052 16264 In base 12: 3a8 568 2389 2689 27b6 29b4 4297 4974 5483 6a35 6b64 7662 86b8 8864 94b4 First 15 Rhonda numbers in base 14: In base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945 67525 68904 91245 99603 125543 In base 14: 4279 6b27 76cd ab27 b7c1 1277d 173da 17547 17bc2 19437 1a873 1b17a 25377 28427 33a75 First 15 Rhonda numbers in base 15: In base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758 31150 33004 33550 37925 39483 In base 15: a97 aec 35e8 4a83 5269 5586 5a1c 5e39 735d 91a8 936a 9ba4 9e1a b385 ba73 First 15 Rhonda numbers in base 16: In base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070 31906 32292 34236 34521 36465 In base 16: 3e8 46e 1a78 3e28 4ca8 4e4b 4f83 5d8a 66b8 718e 7ca2 7e24 85bc 86d9 8e71 First 15 Rhonda numbers in base 18: In base 10: 1470 3000 8918 17025 19402 20650 21120 22156 26522 36549 38354 43281 46035 48768 54229 In base 18: 49c 94c 1998 2g9f 35fg 39d4 3b36 3e6g 49f8 64e9 6a6e 77a9 7g19 8696 956d First 15 Rhonda numbers in base 20: In base 10: 1815 11050 15295 21165 22165 30702 34510 34645 42292 44165 52059 53416 65945 78430 80712 In base 20: 4af 17ca 1i4f 2ci5 2f85 3gf2 465a 46c5 55ec 5a85 6a2j 6dag 84h5 9g1a a1fc First 15 Rhonda numbers in base 21: In base 10: 1632 5390 8512 12992 15678 25038 29412 34017 39552 48895 49147 61376 85078 89590 91798 In base 21: 3ef c4e j67 189e 1ebc 2eg6 33ec 3e2i 45e9 55i7 5697 6d3e 93j7 9e34 9j37 First 15 Rhonda numbers in base 22: In base 10: 2695 4128 7865 28800 31710 37030 71875 74306 117760 117895 121626 126002 131427 175065 192753 In base 22: 5cb 8be g5b 2fb2 2lb8 3ab4 6gb1 6lbc b16g b1cj b96a bi78 c7bl g9fb i25b First 15 Rhonda numbers in base 24: In base 10: 2080 2709 3976 5628 5656 7144 8296 9030 10094 17612 20559 24616 26224 29106 31458 In base 24: 3eg 4gl 6lg 9ic 9jg c9g e9g fg6 hce 16dk 1bgf 1ihg 1lcg 22ci 26ei First 15 Rhonda numbers in base 25: In base 10: 6764 9633 13260 22022 53382 57640 66015 69006 97014 140130 142880 144235 159724 162565 165504 In base 25: ake fa8 l5a 1a5m 3aa7 3h5f 45ff 4aa6 655e 8o55 93f5 95ja a5do aa2f aek4 First 15 Rhonda numbers in base 26: In base 10: 7788 9322 9374 11160 22165 27885 34905 44785 47385 49257 62517 72709 74217 108745 132302 In base 26: bde dke dme gd6 16kd 1f6d 1pgd 2e6d 2i2d 2kmd 3ecd 43ed 45kd 64md 7die First 15 Rhonda numbers in base 27: In base 10: 4797 11844 12078 13200 14841 17750 24320 26883 27477 46455 52750 58581 61009 61446 61500 In base 27: 6fi g6i gf9 i2o k9i o9b 169k 19ni 1aii 29jf 2i9j 2q9i 32ig 337l 339l First 15 Rhonda numbers in base 28: In base 10: 3094 5808 5832 7462 11160 13671 27270 28194 28638 39375 39550 49500 50862 52338 52938 In base 28: 3qe 7bc 7c8 9ee e6g hc7 16lq 17qq 18em 1m67 1mce 273o 28oe 2al6 2bei First 15 Rhonda numbers in base 30: In base 10: 3024 3168 5115 5346 5950 6762 7750 7956 8470 9476 9576 9849 10360 11495 13035 In base 30: 3ao 3fi 5kf 5s6 6ia 7fc 8ia 8p6 9ca afq aj6 as9 bfa cn5 eef First 15 Rhonda numbers in base 32: In base 10: 1944 3600 13520 15876 16732 16849 25410 25752 28951 47472 49610 50968 61596 64904 74005 In base 32: 1so 3gg d6g fg4 gas geh oq2 p4o s8n 1ebg 1gea 1hoo 1s4s 1vc8 288l First 15 Rhonda numbers in base 33: In base 10: 756 7040 7568 13826 24930 30613 59345 63555 64372 131427 227840 264044 313709 336385 344858 In base 33: mu 6fb 6vb cmw mtf s3m 1lgb 1pbu 1q3m 3lml 6b78 7bfb 8o2b 9btg 9jm8 First 15 Rhonda numbers in base 34: In base 10: 5661 14161 15620 16473 22185 37145 125579 134692 135405 138472 140369 177086 250665 255552 295614 In base 34: 4uh c8h dhe e8h j6h w4h 36lh 3ehi 3f4h 3hqo 3jeh 4h6e 6csh 6h28 7hoi First 15 Rhonda numbers in base 35: In base 10: 8232 9476 9633 18634 30954 41905 52215 52440 56889 61992 62146 66339 98260 102180 103305 In base 35: 6p7 7pq 7u8 f7e p9e y7a 17lu 17sa 1bfe 1fl7 1fpl 1j5e 2a7f 2def 2ebk First 15 Rhonda numbers in base 36: In base 10: 1000 4800 5670 8190 10998 12412 13300 15750 16821 23016 51612 52734 67744 70929 75030 In base 36: rs 3pc 4di 6bi 8hi 9ks a9g c5i cz9 hrc 13to 14ou 1g9s 1iq9 1lw6
Raku
Find and show the first 15 so as to display the namesake Rhonda number 25662.
use Prime::Factor;
my @factor-sum;
@factor-sum[1000000] = 42; # Sink a large index to make access thread safe
sub rhonda ($base) {
(1..∞).hyper.map: { $_ if $base * (@factor-sum[$_] //= .&prime-factors.sum) == [×] .polymod($base xx *) }
}
for (flat 2..16, 17..36).grep: { !.&is-prime } -> $b {
put "\nFirst 15 Rhonda numbers to base $b:";
my @rhonda = rhonda($b)[^15];
my $ch = @rhonda[*-1].chars max @rhonda[*-1].base($b).chars;
put "In base 10: " ~ @rhonda».fmt("%{$ch}s").join: ', ';
put $b.fmt("In base %2d: ") ~ @rhonda».base($b)».fmt("%{$ch}s").join: ', ';
}
- Output:
First 15 Rhonda numbers to base 4: In base 10: 10206, 11935, 12150, 16031, 45030, 94185, 113022, 114415, 191149, 244713, 259753, 374782, 392121, 503773, 649902 In base 4: 2133132, 2322133, 2331312, 3322133, 22333212, 112333221, 123211332, 123323233, 232222231, 323233221, 333122221, 1123133332, 1133232321, 1322333131, 2132222232 First 15 Rhonda numbers to base 6: In base 10: 855, 1029, 3813, 5577, 7040, 7304, 15104, 19136, 35350, 36992, 41031, 42009, 60368, 65536, 67821 In base 6: 3543, 4433, 25353, 41453, 52332, 53452, 153532, 224332, 431354, 443132, 513543, 522253, 1143252, 1223224, 1241553 First 15 Rhonda numbers to base 8: In base 10: 1836, 6318, 6622, 10530, 14500, 14739, 17655, 18550, 25398, 25956, 30562, 39215, 39325, 50875, 51429 In base 8: 3454, 14256, 14736, 24442, 34244, 34623, 42367, 44166, 61466, 62544, 73542, 114457, 114635, 143273, 144345 First 15 Rhonda numbers to base 9: In base 10: 15540, 21054, 25331, 44360, 44660, 44733, 47652, 50560, 54944, 76857, 77142, 83334, 83694, 96448, 97944 In base 9: 23276, 31783, 37665, 66758, 67232, 67323, 72326, 76317, 83328, 126376, 126733, 136273, 136723, 156264, 158316 First 15 Rhonda numbers to base 10: In base 10: 1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985, 15625, 15698, 19435, 25284, 25662 In base 10: 1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985, 15625, 15698, 19435, 25284, 25662 First 15 Rhonda numbers to base 12: In base 10: 560, 800, 3993, 4425, 4602, 4888, 7315, 8296, 9315, 11849, 12028, 13034, 14828, 15052, 16264 In base 12: 3A8, 568, 2389, 2689, 27B6, 29B4, 4297, 4974, 5483, 6A35, 6B64, 7662, 86B8, 8864, 94B4 First 15 Rhonda numbers to base 14: In base 10: 11475, 18655, 20565, 29631, 31725, 45387, 58404, 58667, 59950, 63945, 67525, 68904, 91245, 99603, 125543 In base 14: 4279, 6B27, 76CD, AB27, B7C1, 1277D, 173DA, 17547, 17BC2, 19437, 1A873, 1B17A, 25377, 28427, 33A75 First 15 Rhonda numbers to base 15: In base 10: 2392, 2472, 11468, 15873, 17424, 18126, 19152, 20079, 24388, 30758, 31150, 33004, 33550, 37925, 39483 In base 15: A97, AEC, 35E8, 4A83, 5269, 5586, 5A1C, 5E39, 735D, 91A8, 936A, 9BA4, 9E1A, B385, BA73 First 15 Rhonda numbers to base 16: In base 10: 1000, 1134, 6776, 15912, 19624, 20043, 20355, 23946, 26296, 29070, 31906, 32292, 34236, 34521, 36465 In base 16: 3E8, 46E, 1A78, 3E28, 4CA8, 4E4B, 4F83, 5D8A, 66B8, 718E, 7CA2, 7E24, 85BC, 86D9, 8E71 First 15 Rhonda numbers to base 18: In base 10: 1470, 3000, 8918, 17025, 19402, 20650, 21120, 22156, 26522, 36549, 38354, 43281, 46035, 48768, 54229 In base 18: 49C, 94C, 1998, 2G9F, 35FG, 39D4, 3B36, 3E6G, 49F8, 64E9, 6A6E, 77A9, 7G19, 8696, 956D First 15 Rhonda numbers to base 20: In base 10: 1815, 11050, 15295, 21165, 22165, 30702, 34510, 34645, 42292, 44165, 52059, 53416, 65945, 78430, 80712 In base 20: 4AF, 17CA, 1I4F, 2CI5, 2F85, 3GF2, 465A, 46C5, 55EC, 5A85, 6A2J, 6DAG, 84H5, 9G1A, A1FC First 15 Rhonda numbers to base 21: In base 10: 1632, 5390, 8512, 12992, 15678, 25038, 29412, 34017, 39552, 48895, 49147, 61376, 85078, 89590, 91798 In base 21: 3EF, C4E, J67, 189E, 1EBC, 2EG6, 33EC, 3E2I, 45E9, 55I7, 5697, 6D3E, 93J7, 9E34, 9J37 First 15 Rhonda numbers to base 22: In base 10: 2695, 4128, 7865, 28800, 31710, 37030, 71875, 74306, 117760, 117895, 121626, 126002, 131427, 175065, 192753 In base 22: 5CB, 8BE, G5B, 2FB2, 2LB8, 3AB4, 6GB1, 6LBC, B16G, B1CJ, B96A, BI78, C7BL, G9FB, I25B First 15 Rhonda numbers to base 24: In base 10: 2080, 2709, 3976, 5628, 5656, 7144, 8296, 9030, 10094, 17612, 20559, 24616, 26224, 29106, 31458 In base 24: 3EG, 4GL, 6LG, 9IC, 9JG, C9G, E9G, FG6, HCE, 16DK, 1BGF, 1IHG, 1LCG, 22CI, 26EI First 15 Rhonda numbers to base 25: In base 10: 6764, 9633, 13260, 22022, 53382, 57640, 66015, 69006, 97014, 140130, 142880, 144235, 159724, 162565, 165504 In base 25: AKE, FA8, L5A, 1A5M, 3AA7, 3H5F, 45FF, 4AA6, 655E, 8O55, 93F5, 95JA, A5DO, AA2F, AEK4 First 15 Rhonda numbers to base 26: In base 10: 7788, 9322, 9374, 11160, 22165, 27885, 34905, 44785, 47385, 49257, 62517, 72709, 74217, 108745, 132302 In base 26: BDE, DKE, DME, GD6, 16KD, 1F6D, 1PGD, 2E6D, 2I2D, 2KMD, 3ECD, 43ED, 45KD, 64MD, 7DIE First 15 Rhonda numbers to base 27: In base 10: 4797, 11844, 12078, 13200, 14841, 17750, 24320, 26883, 27477, 46455, 52750, 58581, 61009, 61446, 61500 In base 27: 6FI, G6I, GF9, I2O, K9I, O9B, 169K, 19NI, 1AII, 29JF, 2I9J, 2Q9I, 32IG, 337L, 339L First 15 Rhonda numbers to base 28: In base 10: 3094, 5808, 5832, 7462, 11160, 13671, 27270, 28194, 28638, 39375, 39550, 49500, 50862, 52338, 52938 In base 28: 3QE, 7BC, 7C8, 9EE, E6G, HC7, 16LQ, 17QQ, 18EM, 1M67, 1MCE, 273O, 28OE, 2AL6, 2BEI First 15 Rhonda numbers to base 30: In base 10: 3024, 3168, 5115, 5346, 5950, 6762, 7750, 7956, 8470, 9476, 9576, 9849, 10360, 11495, 13035 In base 30: 3AO, 3FI, 5KF, 5S6, 6IA, 7FC, 8IA, 8P6, 9CA, AFQ, AJ6, AS9, BFA, CN5, EEF First 15 Rhonda numbers to base 32: In base 10: 1944, 3600, 13520, 15876, 16732, 16849, 25410, 25752, 28951, 47472, 49610, 50968, 61596, 64904, 74005 In base 32: 1SO, 3GG, D6G, FG4, GAS, GEH, OQ2, P4O, S8N, 1EBG, 1GEA, 1HOO, 1S4S, 1VC8, 288L First 15 Rhonda numbers to base 33: In base 10: 756, 7040, 7568, 13826, 24930, 30613, 59345, 63555, 64372, 131427, 227840, 264044, 313709, 336385, 344858 In base 33: MU, 6FB, 6VB, CMW, MTF, S3M, 1LGB, 1PBU, 1Q3M, 3LML, 6B78, 7BFB, 8O2B, 9BTG, 9JM8 First 15 Rhonda numbers to base 34: In base 10: 5661, 14161, 15620, 16473, 22185, 37145, 125579, 134692, 135405, 138472, 140369, 177086, 250665, 255552, 295614 In base 34: 4UH, C8H, DHE, E8H, J6H, W4H, 36LH, 3EHI, 3F4H, 3HQO, 3JEH, 4H6E, 6CSH, 6H28, 7HOI First 15 Rhonda numbers to base 35: In base 10: 8232, 9476, 9633, 18634, 30954, 41905, 52215, 52440, 56889, 61992, 62146, 66339, 98260, 102180, 103305 In base 35: 6P7, 7PQ, 7U8, F7E, P9E, Y7A, 17LU, 17SA, 1BFE, 1FL7, 1FPL, 1J5E, 2A7F, 2DEF, 2EBK First 15 Rhonda numbers to base 36: In base 10: 1000, 4800, 5670, 8190, 10998, 12412, 13300, 15750, 16821, 23016, 51612, 52734, 67744, 70929, 75030 In base 36: RS, 3PC, 4DI, 6BI, 8HI, 9KS, A9G, C5I, CZ9, HRC, 13TO, 14OU, 1G9S, 1IQ9, 1LW6
Rust
// [dependencies]
// radix_fmt = "1.0"
fn digit_product(base: u32, mut n: u32) -> u32 {
let mut product = 1;
while n != 0 {
product *= n % base;
n /= base;
}
product
}
fn prime_factor_sum(mut n: u32) -> u32 {
let mut sum = 0;
while (n & 1) == 0 {
sum += 2;
n >>= 1;
}
let mut p = 3;
while p * p <= n {
while n % p == 0 {
sum += p;
n /= p;
}
p += 2;
}
if n > 1 {
sum += n;
}
sum
}
fn is_prime(n: u32) -> bool {
if n < 2 {
return false;
}
if n % 2 == 0 {
return n == 2;
}
if n % 3 == 0 {
return n == 3;
}
let mut p = 5;
while p * p <= n {
if n % p == 0 {
return false;
}
p += 2;
if n % p == 0 {
return false;
}
p += 4;
}
true
}
fn is_rhonda(base: u32, n: u32) -> bool {
digit_product(base, n) == base * prime_factor_sum(n)
}
fn main() {
let limit = 15;
for base in 2..=36 {
if is_prime(base) {
continue;
}
println!("First {} Rhonda numbers to base {}:", limit, base);
let numbers: Vec<u32> = (1..).filter(|x| is_rhonda(base, *x)).take(limit).collect();
print!("In base 10:");
for n in &numbers {
print!(" {}", n);
}
print!("\nIn base {}:", base);
for n in &numbers {
print!(" {}", radix_fmt::radix(*n, base as u8));
}
print!("\n\n");
}
}
- Output:
First 15 Rhonda numbers to base 4: In base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713 259753 374782 392121 503773 649902 In base 4: 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221 333122221 1123133332 1133232321 1322333131 2132222232 First 15 Rhonda numbers to base 6: In base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992 41031 42009 60368 65536 67821 In base 6: 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132 513543 522253 1143252 1223224 1241553 First 15 Rhonda numbers to base 8: In base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956 30562 39215 39325 50875 51429 In base 8: 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544 73542 114457 114635 143273 144345 First 15 Rhonda numbers to base 9: In base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857 77142 83334 83694 96448 97944 In base 9: 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376 126733 136273 136723 156264 158316 First 15 Rhonda numbers to base 10: In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662 In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662 First 15 Rhonda numbers to base 12: In base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849 12028 13034 14828 15052 16264 In base 12: 3a8 568 2389 2689 27b6 29b4 4297 4974 5483 6a35 6b64 7662 86b8 8864 94b4 First 15 Rhonda numbers to base 14: In base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945 67525 68904 91245 99603 125543 In base 14: 4279 6b27 76cd ab27 b7c1 1277d 173da 17547 17bc2 19437 1a873 1b17a 25377 28427 33a75 First 15 Rhonda numbers to base 15: In base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758 31150 33004 33550 37925 39483 In base 15: a97 aec 35e8 4a83 5269 5586 5a1c 5e39 735d 91a8 936a 9ba4 9e1a b385 ba73 First 15 Rhonda numbers to base 16: In base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070 31906 32292 34236 34521 36465 In base 16: 3e8 46e 1a78 3e28 4ca8 4e4b 4f83 5d8a 66b8 718e 7ca2 7e24 85bc 86d9 8e71 First 15 Rhonda numbers to base 18: In base 10: 1470 3000 8918 17025 19402 20650 21120 22156 26522 36549 38354 43281 46035 48768 54229 In base 18: 49c 94c 1998 2g9f 35fg 39d4 3b36 3e6g 49f8 64e9 6a6e 77a9 7g19 8696 956d First 15 Rhonda numbers to base 20: In base 10: 1815 11050 15295 21165 22165 30702 34510 34645 42292 44165 52059 53416 65945 78430 80712 In base 20: 4af 17ca 1i4f 2ci5 2f85 3gf2 465a 46c5 55ec 5a85 6a2j 6dag 84h5 9g1a a1fc First 15 Rhonda numbers to base 21: In base 10: 1632 5390 8512 12992 15678 25038 29412 34017 39552 48895 49147 61376 85078 89590 91798 In base 21: 3ef c4e j67 189e 1ebc 2eg6 33ec 3e2i 45e9 55i7 5697 6d3e 93j7 9e34 9j37 First 15 Rhonda numbers to base 22: In base 10: 2695 4128 7865 28800 31710 37030 71875 74306 117760 117895 121626 126002 131427 175065 192753 In base 22: 5cb 8be g5b 2fb2 2lb8 3ab4 6gb1 6lbc b16g b1cj b96a bi78 c7bl g9fb i25b First 15 Rhonda numbers to base 24: In base 10: 2080 2709 3976 5628 5656 7144 8296 9030 10094 17612 20559 24616 26224 29106 31458 In base 24: 3eg 4gl 6lg 9ic 9jg c9g e9g fg6 hce 16dk 1bgf 1ihg 1lcg 22ci 26ei First 15 Rhonda numbers to base 25: In base 10: 6764 9633 13260 22022 53382 57640 66015 69006 97014 140130 142880 144235 159724 162565 165504 In base 25: ake fa8 l5a 1a5m 3aa7 3h5f 45ff 4aa6 655e 8o55 93f5 95ja a5do aa2f aek4 First 15 Rhonda numbers to base 26: In base 10: 7788 9322 9374 11160 22165 27885 34905 44785 47385 49257 62517 72709 74217 108745 132302 In base 26: bde dke dme gd6 16kd 1f6d 1pgd 2e6d 2i2d 2kmd 3ecd 43ed 45kd 64md 7die First 15 Rhonda numbers to base 27: In base 10: 4797 11844 12078 13200 14841 17750 24320 26883 27477 46455 52750 58581 61009 61446 61500 In base 27: 6fi g6i gf9 i2o k9i o9b 169k 19ni 1aii 29jf 2i9j 2q9i 32ig 337l 339l First 15 Rhonda numbers to base 28: In base 10: 3094 5808 5832 7462 11160 13671 27270 28194 28638 39375 39550 49500 50862 52338 52938 In base 28: 3qe 7bc 7c8 9ee e6g hc7 16lq 17qq 18em 1m67 1mce 273o 28oe 2al6 2bei First 15 Rhonda numbers to base 30: In base 10: 3024 3168 5115 5346 5950 6762 7750 7956 8470 9476 9576 9849 10360 11495 13035 In base 30: 3ao 3fi 5kf 5s6 6ia 7fc 8ia 8p6 9ca afq aj6 as9 bfa cn5 eef First 15 Rhonda numbers to base 32: In base 10: 1944 3600 13520 15876 16732 16849 25410 25752 28951 47472 49610 50968 61596 64904 74005 In base 32: 1so 3gg d6g fg4 gas geh oq2 p4o s8n 1ebg 1gea 1hoo 1s4s 1vc8 288l First 15 Rhonda numbers to base 33: In base 10: 756 7040 7568 13826 24930 30613 59345 63555 64372 131427 227840 264044 313709 336385 344858 In base 33: mu 6fb 6vb cmw mtf s3m 1lgb 1pbu 1q3m 3lml 6b78 7bfb 8o2b 9btg 9jm8 First 15 Rhonda numbers to base 34: In base 10: 5661 14161 15620 16473 22185 37145 125579 134692 135405 138472 140369 177086 250665 255552 295614 In base 34: 4uh c8h dhe e8h j6h w4h 36lh 3ehi 3f4h 3hqo 3jeh 4h6e 6csh 6h28 7hoi First 15 Rhonda numbers to base 35: In base 10: 8232 9476 9633 18634 30954 41905 52215 52440 56889 61992 62146 66339 98260 102180 103305 In base 35: 6p7 7pq 7u8 f7e p9e y7a 17lu 17sa 1bfe 1fl7 1fpl 1j5e 2a7f 2def 2ebk First 15 Rhonda numbers to base 36: In base 10: 1000 4800 5670 8190 10998 12412 13300 15750 16821 23016 51612 52734 67744 70929 75030 In base 36: rs 3pc 4di 6bi 8hi 9ks a9g c5i cz9 hrc 13to 14ou 1g9s 1iq9 1lw6
Sidef
func is_rhonda_number(n, base = 10) {
base.is_composite || return false
n > 0 || return false
n.digits(base).prod == base*n.factor.sum
}
for b in (2..16 -> grep { .is_composite }) {
say ("First 10 Rhonda numbers to base #{b}: ",
10.by { is_rhonda_number(_, b) })
}
- Output:
First 10 Rhonda numbers to base 4: [10206, 11935, 12150, 16031, 45030, 94185, 113022, 114415, 191149, 244713] First 10 Rhonda numbers to base 6: [855, 1029, 3813, 5577, 7040, 7304, 15104, 19136, 35350, 36992] First 10 Rhonda numbers to base 8: [1836, 6318, 6622, 10530, 14500, 14739, 17655, 18550, 25398, 25956] First 10 Rhonda numbers to base 9: [15540, 21054, 25331, 44360, 44660, 44733, 47652, 50560, 54944, 76857] First 10 Rhonda numbers to base 10: [1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985] First 10 Rhonda numbers to base 12: [560, 800, 3993, 4425, 4602, 4888, 7315, 8296, 9315, 11849] First 10 Rhonda numbers to base 14: [11475, 18655, 20565, 29631, 31725, 45387, 58404, 58667, 59950, 63945] First 10 Rhonda numbers to base 15: [2392, 2472, 11468, 15873, 17424, 18126, 19152, 20079, 24388, 30758] First 10 Rhonda numbers to base 16: [1000, 1134, 6776, 15912, 19624, 20043, 20355, 23946, 26296, 29070]
Swift
func digitProduct(base: Int, num: Int) -> Int {
var product = 1
var n = num
while n != 0 {
product *= n % base
n /= base
}
return product
}
func primeFactorSum(_ num: Int) -> Int {
var sum = 0
var n = num
while (n & 1) == 0 {
sum += 2
n >>= 1
}
var p = 3
while p * p <= n {
while n % p == 0 {
sum += p
n /= p
}
p += 2
}
if n > 1 {
sum += n
}
return sum
}
func isPrime(_ n: Int) -> Bool {
if n < 2 {
return false
}
if n % 2 == 0 {
return n == 2
}
if n % 3 == 0 {
return n == 3
}
var p = 5
while p * p <= n {
if n % p == 0 {
return false
}
p += 2
if n % p == 0 {
return false
}
p += 4
}
return true
}
func isRhonda(base: Int, num: Int) -> Bool {
return digitProduct(base: base, num: num) == base * primeFactorSum(num)
}
let limit = 15
for base in 2...36 {
if isPrime(base) {
continue
}
print("First \(limit) Rhonda numbers to base \(base):")
let numbers = Array((1...).lazy.filter{ isRhonda(base: base, num: $0) }.prefix(limit))
print("In base 10:", terminator: "")
for n in numbers {
print(" \(n)", terminator: "")
}
print("\nIn base \(base):", terminator: "")
for n in numbers {
print(" \(String(n, radix: base))", terminator: "")
}
print("\n")
}
- Output:
First 15 Rhonda numbers to base 4: In base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713 259753 374782 392121 503773 649902 In base 4: 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221 333122221 1123133332 1133232321 1322333131 2132222232 First 15 Rhonda numbers to base 6: In base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992 41031 42009 60368 65536 67821 In base 6: 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132 513543 522253 1143252 1223224 1241553 First 15 Rhonda numbers to base 8: In base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956 30562 39215 39325 50875 51429 In base 8: 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544 73542 114457 114635 143273 144345 First 15 Rhonda numbers to base 9: In base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857 77142 83334 83694 96448 97944 In base 9: 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376 126733 136273 136723 156264 158316 First 15 Rhonda numbers to base 10: In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662 In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662 First 15 Rhonda numbers to base 12: In base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849 12028 13034 14828 15052 16264 In base 12: 3a8 568 2389 2689 27b6 29b4 4297 4974 5483 6a35 6b64 7662 86b8 8864 94b4 First 15 Rhonda numbers to base 14: In base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945 67525 68904 91245 99603 125543 In base 14: 4279 6b27 76cd ab27 b7c1 1277d 173da 17547 17bc2 19437 1a873 1b17a 25377 28427 33a75 First 15 Rhonda numbers to base 15: In base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758 31150 33004 33550 37925 39483 In base 15: a97 aec 35e8 4a83 5269 5586 5a1c 5e39 735d 91a8 936a 9ba4 9e1a b385 ba73 First 15 Rhonda numbers to base 16: In base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070 31906 32292 34236 34521 36465 In base 16: 3e8 46e 1a78 3e28 4ca8 4e4b 4f83 5d8a 66b8 718e 7ca2 7e24 85bc 86d9 8e71 First 15 Rhonda numbers to base 18: In base 10: 1470 3000 8918 17025 19402 20650 21120 22156 26522 36549 38354 43281 46035 48768 54229 In base 18: 49c 94c 1998 2g9f 35fg 39d4 3b36 3e6g 49f8 64e9 6a6e 77a9 7g19 8696 956d First 15 Rhonda numbers to base 20: In base 10: 1815 11050 15295 21165 22165 30702 34510 34645 42292 44165 52059 53416 65945 78430 80712 In base 20: 4af 17ca 1i4f 2ci5 2f85 3gf2 465a 46c5 55ec 5a85 6a2j 6dag 84h5 9g1a a1fc First 15 Rhonda numbers to base 21: In base 10: 1632 5390 8512 12992 15678 25038 29412 34017 39552 48895 49147 61376 85078 89590 91798 In base 21: 3ef c4e j67 189e 1ebc 2eg6 33ec 3e2i 45e9 55i7 5697 6d3e 93j7 9e34 9j37 First 15 Rhonda numbers to base 22: In base 10: 2695 4128 7865 28800 31710 37030 71875 74306 117760 117895 121626 126002 131427 175065 192753 In base 22: 5cb 8be g5b 2fb2 2lb8 3ab4 6gb1 6lbc b16g b1cj b96a bi78 c7bl g9fb i25b First 15 Rhonda numbers to base 24: In base 10: 2080 2709 3976 5628 5656 7144 8296 9030 10094 17612 20559 24616 26224 29106 31458 In base 24: 3eg 4gl 6lg 9ic 9jg c9g e9g fg6 hce 16dk 1bgf 1ihg 1lcg 22ci 26ei First 15 Rhonda numbers to base 25: In base 10: 6764 9633 13260 22022 53382 57640 66015 69006 97014 140130 142880 144235 159724 162565 165504 In base 25: ake fa8 l5a 1a5m 3aa7 3h5f 45ff 4aa6 655e 8o55 93f5 95ja a5do aa2f aek4 First 15 Rhonda numbers to base 26: In base 10: 7788 9322 9374 11160 22165 27885 34905 44785 47385 49257 62517 72709 74217 108745 132302 In base 26: bde dke dme gd6 16kd 1f6d 1pgd 2e6d 2i2d 2kmd 3ecd 43ed 45kd 64md 7die First 15 Rhonda numbers to base 27: In base 10: 4797 11844 12078 13200 14841 17750 24320 26883 27477 46455 52750 58581 61009 61446 61500 In base 27: 6fi g6i gf9 i2o k9i o9b 169k 19ni 1aii 29jf 2i9j 2q9i 32ig 337l 339l First 15 Rhonda numbers to base 28: In base 10: 3094 5808 5832 7462 11160 13671 27270 28194 28638 39375 39550 49500 50862 52338 52938 In base 28: 3qe 7bc 7c8 9ee e6g hc7 16lq 17qq 18em 1m67 1mce 273o 28oe 2al6 2bei First 15 Rhonda numbers to base 30: In base 10: 3024 3168 5115 5346 5950 6762 7750 7956 8470 9476 9576 9849 10360 11495 13035 In base 30: 3ao 3fi 5kf 5s6 6ia 7fc 8ia 8p6 9ca afq aj6 as9 bfa cn5 eef First 15 Rhonda numbers to base 32: In base 10: 1944 3600 13520 15876 16732 16849 25410 25752 28951 47472 49610 50968 61596 64904 74005 In base 32: 1so 3gg d6g fg4 gas geh oq2 p4o s8n 1ebg 1gea 1hoo 1s4s 1vc8 288l First 15 Rhonda numbers to base 33: In base 10: 756 7040 7568 13826 24930 30613 59345 63555 64372 131427 227840 264044 313709 336385 344858 In base 33: mu 6fb 6vb cmw mtf s3m 1lgb 1pbu 1q3m 3lml 6b78 7bfb 8o2b 9btg 9jm8 First 15 Rhonda numbers to base 34: In base 10: 5661 14161 15620 16473 22185 37145 125579 134692 135405 138472 140369 177086 250665 255552 295614 In base 34: 4uh c8h dhe e8h j6h w4h 36lh 3ehi 3f4h 3hqo 3jeh 4h6e 6csh 6h28 7hoi First 15 Rhonda numbers to base 35: In base 10: 8232 9476 9633 18634 30954 41905 52215 52440 56889 61992 62146 66339 98260 102180 103305 In base 35: 6p7 7pq 7u8 f7e p9e y7a 17lu 17sa 1bfe 1fl7 1fpl 1j5e 2a7f 2def 2ebk First 15 Rhonda numbers to base 36: In base 10: 1000 4800 5670 8190 10998 12412 13300 15750 16821 23016 51612 52734 67744 70929 75030 In base 36: rs 3pc 4di 6bi 8hi 9ks a9g c5i cz9 hrc 13to 14ou 1g9s 1iq9 1lw6
Wren
import "./math" for Math, Int, Nums
import "./fmt" for Fmt, Conv
for (b in 2..36) {
if (Int.isPrime(b)) continue
var count = 0
var rhonda = []
var n = 1
while (count < 15) {
var digits = Int.digits(n, b)
if (!digits.contains(0)) {
if (b != 10 || (digits.contains(5) && digits.any { |d| d % 2 == 0 })) {
var calc1 = Nums.prod(digits)
var calc2 = b * Nums.sum(Int.primeFactors(n))
if (calc1 == calc2) {
rhonda.add(n)
count = count + 1
}
}
}
n = n + 1
}
if (rhonda.count > 0) {
System.print("\nFirst 15 Rhonda numbers in base %(b):")
var rhonda2 = rhonda.map { |r| r.toString }.toList
var rhonda3 = rhonda.map { |r| Conv.Itoa(r, b) }.toList
var maxLen2 = Nums.max(rhonda2.map { |r| r.count })
var maxLen3 = Nums.max(rhonda3.map { |r| r.count })
var maxLen = Math.max(maxLen2, maxLen3) + 1
Fmt.print("In base 10: $*s", maxLen, rhonda2)
Fmt.print("In base $-2d: $*s", b, maxLen, rhonda3)
}
}
- Output:
First 15 Rhonda numbers in base 4: In base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713 259753 374782 392121 503773 649902 In base 4 : 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221 333122221 1123133332 1133232321 1322333131 2132222232 First 15 Rhonda numbers in base 6: In base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992 41031 42009 60368 65536 67821 In base 6 : 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132 513543 522253 1143252 1223224 1241553 First 15 Rhonda numbers in base 8: In base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956 30562 39215 39325 50875 51429 In base 8 : 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544 73542 114457 114635 143273 144345 First 15 Rhonda numbers in base 9: In base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857 77142 83334 83694 96448 97944 In base 9 : 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376 126733 136273 136723 156264 158316 First 15 Rhonda numbers in base 10: In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662 In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662 First 15 Rhonda numbers in base 12: In base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849 12028 13034 14828 15052 16264 In base 12: 3A8 568 2389 2689 27B6 29B4 4297 4974 5483 6A35 6B64 7662 86B8 8864 94B4 First 15 Rhonda numbers in base 14: In base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945 67525 68904 91245 99603 125543 In base 14: 4279 6B27 76CD AB27 B7C1 1277D 173DA 17547 17BC2 19437 1A873 1B17A 25377 28427 33A75 First 15 Rhonda numbers in base 15: In base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758 31150 33004 33550 37925 39483 In base 15: A97 AEC 35E8 4A83 5269 5586 5A1C 5E39 735D 91A8 936A 9BA4 9E1A B385 BA73 First 15 Rhonda numbers in base 16: In base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070 31906 32292 34236 34521 36465 In base 16: 3E8 46E 1A78 3E28 4CA8 4E4B 4F83 5D8A 66B8 718E 7CA2 7E24 85BC 86D9 8E71 First 15 Rhonda numbers in base 18: In base 10: 1470 3000 8918 17025 19402 20650 21120 22156 26522 36549 38354 43281 46035 48768 54229 In base 18: 49C 94C 1998 2G9F 35FG 39D4 3B36 3E6G 49F8 64E9 6A6E 77A9 7G19 8696 956D First 15 Rhonda numbers in base 20: In base 10: 1815 11050 15295 21165 22165 30702 34510 34645 42292 44165 52059 53416 65945 78430 80712 In base 20: 4AF 17CA 1I4F 2CI5 2F85 3GF2 465A 46C5 55EC 5A85 6A2J 6DAG 84H5 9G1A A1FC First 15 Rhonda numbers in base 21: In base 10: 1632 5390 8512 12992 15678 25038 29412 34017 39552 48895 49147 61376 85078 89590 91798 In base 21: 3EF C4E J67 189E 1EBC 2EG6 33EC 3E2I 45E9 55I7 5697 6D3E 93J7 9E34 9J37 First 15 Rhonda numbers in base 22: In base 10: 2695 4128 7865 28800 31710 37030 71875 74306 117760 117895 121626 126002 131427 175065 192753 In base 22: 5CB 8BE G5B 2FB2 2LB8 3AB4 6GB1 6LBC B16G B1CJ B96A BI78 C7BL G9FB I25B First 15 Rhonda numbers in base 24: In base 10: 2080 2709 3976 5628 5656 7144 8296 9030 10094 17612 20559 24616 26224 29106 31458 In base 24: 3EG 4GL 6LG 9IC 9JG C9G E9G FG6 HCE 16DK 1BGF 1IHG 1LCG 22CI 26EI First 15 Rhonda numbers in base 25: In base 10: 6764 9633 13260 22022 53382 57640 66015 69006 97014 140130 142880 144235 159724 162565 165504 In base 25: AKE FA8 L5A 1A5M 3AA7 3H5F 45FF 4AA6 655E 8O55 93F5 95JA A5DO AA2F AEK4 First 15 Rhonda numbers in base 26: In base 10: 7788 9322 9374 11160 22165 27885 34905 44785 47385 49257 62517 72709 74217 108745 132302 In base 26: BDE DKE DME GD6 16KD 1F6D 1PGD 2E6D 2I2D 2KMD 3ECD 43ED 45KD 64MD 7DIE First 15 Rhonda numbers in base 27: In base 10: 4797 11844 12078 13200 14841 17750 24320 26883 27477 46455 52750 58581 61009 61446 61500 In base 27: 6FI G6I GF9 I2O K9I O9B 169K 19NI 1AII 29JF 2I9J 2Q9I 32IG 337L 339L First 15 Rhonda numbers in base 28: In base 10: 3094 5808 5832 7462 11160 13671 27270 28194 28638 39375 39550 49500 50862 52338 52938 In base 28: 3QE 7BC 7C8 9EE E6G HC7 16LQ 17QQ 18EM 1M67 1MCE 273O 28OE 2AL6 2BEI First 15 Rhonda numbers in base 30: In base 10: 3024 3168 5115 5346 5950 6762 7750 7956 8470 9476 9576 9849 10360 11495 13035 In base 30: 3AO 3FI 5KF 5S6 6IA 7FC 8IA 8P6 9CA AFQ AJ6 AS9 BFA CN5 EEF First 15 Rhonda numbers in base 32: In base 10: 1944 3600 13520 15876 16732 16849 25410 25752 28951 47472 49610 50968 61596 64904 74005 In base 32: 1SO 3GG D6G FG4 GAS GEH OQ2 P4O S8N 1EBG 1GEA 1HOO 1S4S 1VC8 288L First 15 Rhonda numbers in base 33: In base 10: 756 7040 7568 13826 24930 30613 59345 63555 64372 131427 227840 264044 313709 336385 344858 In base 33: MU 6FB 6VB CMW MTF S3M 1LGB 1PBU 1Q3M 3LML 6B78 7BFB 8O2B 9BTG 9JM8 First 15 Rhonda numbers in base 34: In base 10: 5661 14161 15620 16473 22185 37145 125579 134692 135405 138472 140369 177086 250665 255552 295614 In base 34: 4UH C8H DHE E8H J6H W4H 36LH 3EHI 3F4H 3HQO 3JEH 4H6E 6CSH 6H28 7HOI First 15 Rhonda numbers in base 35: In base 10: 8232 9476 9633 18634 30954 41905 52215 52440 56889 61992 62146 66339 98260 102180 103305 In base 35: 6P7 7PQ 7U8 F7E P9E Y7A 17LU 17SA 1BFE 1FL7 1FPL 1J5E 2A7F 2DEF 2EBK First 15 Rhonda numbers in base 36: In base 10: 1000 4800 5670 8190 10998 12412 13300 15750 16821 23016 51612 52734 67744 70929 75030 In base 36: RS 3PC 4DI 6BI 8HI 9KS A9G C5I CZ9 HRC 13TO 14OU 1G9S 1IQ9 1LW6