Rhonda numbers
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.
You are encouraged to solve this task according to the task description, using any language you may know.
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
C++
<lang cpp>#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"; }
}</lang>
- 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
<lang 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</lang>
- 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
Go
<lang 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) } }
}</lang>
- 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
<lang J>tobase=: (a.{~;48 97(+ i.)each 10 26) {~ #.inv isrhonda=: (*/@:(#.inv) = (* +/@q:))"0
task=: Template:For base.(
task
</lang>
- 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
Java
<lang 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); }
}</lang>
- 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
Julia
<lang 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)
</lang>
- 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]
Perl
<lang 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
} </lang>
- 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. <lang perl6>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: ', ';
}</lang>
- 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
<lang 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"); }
}</lang>
- 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
<lang ruby>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) })
}</lang>
- 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]
Wren
<lang ecmascript>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) }
}</lang>
- 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