Rhonda numbers
Find and show the first 15 so as to display the namesake Rhonda number 25662.
use Prime::Factor;
my @factor-sum;
@factor-sum[1000000] = 42; # Sink a large index to make access thread safe
sub rhonda ($base) {
(1..∞).hyper.map: { $_ if $base * (@factor-sum[$_] //= .&prime-factors.sum) == [×] .polymod($base xx *) }
}
for (flat 2..16, 17..36).grep: { !.&is-prime } -> $b {
put "\nFirst 15 Rhonda numbers to base $b:";
my @rhonda = rhonda($b)[^15];
my $ch = @rhonda[*-1].chars max @rhonda[*-1].base($b).chars;
put "In base 10: " ~ @rhonda».fmt("%{$ch}s").join: ', ';
put $b.fmt("In base %2d: ") ~ @rhonda».base($b)».fmt("%{$ch}s").join: ', ';
}Output:
First 15 Rhonda numbers to base 4:
In base 10: 10206, 11935, 12150, 16031, 45030, 94185, 113022, 114415, 191149, 244713, 259753, 374782, 392121, 503773, 649902
In base 4: 2133132, 2322133, 2331312, 3322133, 22333212, 112333221, 123211332, 123323233, 232222231, 323233221, 333122221, 1123133332, 1133232321, 1322333131, 2132222232
First 15 Rhonda numbers to base 6:
In base 10: 855, 1029, 3813, 5577, 7040, 7304, 15104, 19136, 35350, 36992, 41031, 42009, 60368, 65536, 67821
In base 6: 3543, 4433, 25353, 41453, 52332, 53452, 153532, 224332, 431354, 443132, 513543, 522253, 1143252, 1223224, 1241553
First 15 Rhonda numbers to base 8:
In base 10: 1836, 6318, 6622, 10530, 14500, 14739, 17655, 18550, 25398, 25956, 30562, 39215, 39325, 50875, 51429
In base 8: 3454, 14256, 14736, 24442, 34244, 34623, 42367, 44166, 61466, 62544, 73542, 114457, 114635, 143273, 144345
First 15 Rhonda numbers to base 9:
In base 10: 15540, 21054, 25331, 44360, 44660, 44733, 47652, 50560, 54944, 76857, 77142, 83334, 83694, 96448, 97944
In base 9: 23276, 31783, 37665, 66758, 67232, 67323, 72326, 76317, 83328, 126376, 126733, 136273, 136723, 156264, 158316
First 15 Rhonda numbers to base 10:
In base 10: 1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985, 15625, 15698, 19435, 25284, 25662
In base 10: 1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985, 15625, 15698, 19435, 25284, 25662
First 15 Rhonda numbers to base 12:
In base 10: 560, 800, 3993, 4425, 4602, 4888, 7315, 8296, 9315, 11849, 12028, 13034, 14828, 15052, 16264
In base 12: 3A8, 568, 2389, 2689, 27B6, 29B4, 4297, 4974, 5483, 6A35, 6B64, 7662, 86B8, 8864, 94B4
First 15 Rhonda numbers to base 14:
In base 10: 11475, 18655, 20565, 29631, 31725, 45387, 58404, 58667, 59950, 63945, 67525, 68904, 91245, 99603, 125543
In base 14: 4279, 6B27, 76CD, AB27, B7C1, 1277D, 173DA, 17547, 17BC2, 19437, 1A873, 1B17A, 25377, 28427, 33A75
First 15 Rhonda numbers to base 15:
In base 10: 2392, 2472, 11468, 15873, 17424, 18126, 19152, 20079, 24388, 30758, 31150, 33004, 33550, 37925, 39483
In base 15: A97, AEC, 35E8, 4A83, 5269, 5586, 5A1C, 5E39, 735D, 91A8, 936A, 9BA4, 9E1A, B385, BA73
First 15 Rhonda numbers to base 16:
In base 10: 1000, 1134, 6776, 15912, 19624, 20043, 20355, 23946, 26296, 29070, 31906, 32292, 34236, 34521, 36465
In base 16: 3E8, 46E, 1A78, 3E28, 4CA8, 4E4B, 4F83, 5D8A, 66B8, 718E, 7CA2, 7E24, 85BC, 86D9, 8E71
First 15 Rhonda numbers to base 18:
In base 10: 1470, 3000, 8918, 17025, 19402, 20650, 21120, 22156, 26522, 36549, 38354, 43281, 46035, 48768, 54229
In base 18: 49C, 94C, 1998, 2G9F, 35FG, 39D4, 3B36, 3E6G, 49F8, 64E9, 6A6E, 77A9, 7G19, 8696, 956D
First 15 Rhonda numbers to base 20:
In base 10: 1815, 11050, 15295, 21165, 22165, 30702, 34510, 34645, 42292, 44165, 52059, 53416, 65945, 78430, 80712
In base 20: 4AF, 17CA, 1I4F, 2CI5, 2F85, 3GF2, 465A, 46C5, 55EC, 5A85, 6A2J, 6DAG, 84H5, 9G1A, A1FC
First 15 Rhonda numbers to base 21:
In base 10: 1632, 5390, 8512, 12992, 15678, 25038, 29412, 34017, 39552, 48895, 49147, 61376, 85078, 89590, 91798
In base 21: 3EF, C4E, J67, 189E, 1EBC, 2EG6, 33EC, 3E2I, 45E9, 55I7, 5697, 6D3E, 93J7, 9E34, 9J37
First 15 Rhonda numbers to base 22:
In base 10: 2695, 4128, 7865, 28800, 31710, 37030, 71875, 74306, 117760, 117895, 121626, 126002, 131427, 175065, 192753
In base 22: 5CB, 8BE, G5B, 2FB2, 2LB8, 3AB4, 6GB1, 6LBC, B16G, B1CJ, B96A, BI78, C7BL, G9FB, I25B
First 15 Rhonda numbers to base 24:
In base 10: 2080, 2709, 3976, 5628, 5656, 7144, 8296, 9030, 10094, 17612, 20559, 24616, 26224, 29106, 31458
In base 24: 3EG, 4GL, 6LG, 9IC, 9JG, C9G, E9G, FG6, HCE, 16DK, 1BGF, 1IHG, 1LCG, 22CI, 26EI
First 15 Rhonda numbers to base 25:
In base 10: 6764, 9633, 13260, 22022, 53382, 57640, 66015, 69006, 97014, 140130, 142880, 144235, 159724, 162565, 165504
In base 25: AKE, FA8, L5A, 1A5M, 3AA7, 3H5F, 45FF, 4AA6, 655E, 8O55, 93F5, 95JA, A5DO, AA2F, AEK4
First 15 Rhonda numbers to base 26:
In base 10: 7788, 9322, 9374, 11160, 22165, 27885, 34905, 44785, 47385, 49257, 62517, 72709, 74217, 108745, 132302
In base 26: BDE, DKE, DME, GD6, 16KD, 1F6D, 1PGD, 2E6D, 2I2D, 2KMD, 3ECD, 43ED, 45KD, 64MD, 7DIE
First 15 Rhonda numbers to base 27:
In base 10: 4797, 11844, 12078, 13200, 14841, 17750, 24320, 26883, 27477, 46455, 52750, 58581, 61009, 61446, 61500
In base 27: 6FI, G6I, GF9, I2O, K9I, O9B, 169K, 19NI, 1AII, 29JF, 2I9J, 2Q9I, 32IG, 337L, 339L
First 15 Rhonda numbers to base 28:
In base 10: 3094, 5808, 5832, 7462, 11160, 13671, 27270, 28194, 28638, 39375, 39550, 49500, 50862, 52338, 52938
In base 28: 3QE, 7BC, 7C8, 9EE, E6G, HC7, 16LQ, 17QQ, 18EM, 1M67, 1MCE, 273O, 28OE, 2AL6, 2BEI
First 15 Rhonda numbers to base 30:
In base 10: 3024, 3168, 5115, 5346, 5950, 6762, 7750, 7956, 8470, 9476, 9576, 9849, 10360, 11495, 13035
In base 30: 3AO, 3FI, 5KF, 5S6, 6IA, 7FC, 8IA, 8P6, 9CA, AFQ, AJ6, AS9, BFA, CN5, EEF
First 15 Rhonda numbers to base 32:
In base 10: 1944, 3600, 13520, 15876, 16732, 16849, 25410, 25752, 28951, 47472, 49610, 50968, 61596, 64904, 74005
In base 32: 1SO, 3GG, D6G, FG4, GAS, GEH, OQ2, P4O, S8N, 1EBG, 1GEA, 1HOO, 1S4S, 1VC8, 288L
First 15 Rhonda numbers to base 33:
In base 10: 756, 7040, 7568, 13826, 24930, 30613, 59345, 63555, 64372, 131427, 227840, 264044, 313709, 336385, 344858
In base 33: MU, 6FB, 6VB, CMW, MTF, S3M, 1LGB, 1PBU, 1Q3M, 3LML, 6B78, 7BFB, 8O2B, 9BTG, 9JM8
First 15 Rhonda numbers to base 34:
In base 10: 5661, 14161, 15620, 16473, 22185, 37145, 125579, 134692, 135405, 138472, 140369, 177086, 250665, 255552, 295614
In base 34: 4UH, C8H, DHE, E8H, J6H, W4H, 36LH, 3EHI, 3F4H, 3HQO, 3JEH, 4H6E, 6CSH, 6H28, 7HOI
First 15 Rhonda numbers to base 35:
In base 10: 8232, 9476, 9633, 18634, 30954, 41905, 52215, 52440, 56889, 61992, 62146, 66339, 98260, 102180, 103305
In base 35: 6P7, 7PQ, 7U8, F7E, P9E, Y7A, 17LU, 17SA, 1BFE, 1FL7, 1FPL, 1J5E, 2A7F, 2DEF, 2EBK
First 15 Rhonda numbers to base 36:
In base 10: 1000, 4800, 5670, 8190, 10998, 12412, 13300, 15750, 16821, 23016, 51612, 52734, 67744, 70929, 75030
In base 36: RS, 3PC, 4DI, 6BI, 8HI, 9KS, A9G, C5I, CZ9, HRC, 13TO, 14OU, 1G9S, 1IQ9, 1LW6Last updated