Rhonda numbers: Difference between revisions
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task''
</lang>
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<pre style="height:40ex;overflow:scroll;">
First 15 Rhondas in base 4:
In base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713 259753 374782 392121 503773 649902
Line 164 ⟶ 166:
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
</pre>▼
=={{header|Julia}}==
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displayrhondas(2, 16, 15)
</lang>{{out}}
<pre style="height:40ex;overflow:scroll;">
▲<pre>
First 15 Rhondas in base 4:
In base 10: [10206, 11935, 12150, 16031, 45030, 94185, 113022, 114415, 191149, 244713, 259753, 374782, 392121, 503773, 649902]
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Revision as of 04:49, 12 February 2022
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
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
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]
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
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