Se desarrollan temas de matemáticas con el uso del software Wolfram Mathematica. . germanalvarado@usta.edu.co
viernes, 24 de febrero de 2017
Números Vampiros
Introducidos en 1994 por Clifford A. Pickover, un número v es vampiro si :
1. tiene un número par n de cifras,
2. se obtiene al multiplicar dos enteros x e y (los colmillos del vampiro), ambos con n/2 dígitos,
3. los enteros x e y no terminan simultáneamente en ceros, y
4. v está formado por los dígitos de x e y, en cualquier orden y la misma cantidad.
Por ejemplo, 1260 es un número vampiro, pues con 21 y 60 se cumplen las cuatro condiciones anteriores.
En Mathematica
Buscamos números vampiros de 2, 4 y 6 cifras, y mostramos el Número Vampiro y sus dos colmillos:
vam = {};
SetSharedVariable[vam]
Do[ParallelDo[aaa = Permutations[IntegerDigits[n]];
Do[If[FromDigits[aaa[[p, 1 ;; k/2]]]*
FromDigits[aaa[[p, (k/2) + 1 ;; k]]] == n &&
Nand[IntegerQ[FromDigits[aaa[[p, 1 ;; k/2]]]/10],
IntegerQ[FromDigits[aaa[[p, (k/2) + 1 ;; k]]]/10]],
AppendTo[
vam, {n, FromDigits[aaa[[p, 1 ;; k/2]]],
FromDigits[aaa[[p, (k/2) + 1 ;; k]]]}]; n++], {p,
Length[aaa]}], {n, 10^(k - 1), 10^k - 1}], {k, 2, 6, 2}]
van
{{1395, 15, 93}, {1260, 21, 60}, {1435, 41, 35}, {1530, 51, 30}, {1827, 87, 21}, {2187, 27, 81}, {6880, 86, 80}, {102510, 201, 510}, {108135, 135, 801}, {104260, 401, 260}, {105210, 501, 210},
{105264, 516, 204}, {110758, 158, 701}, {105750, 150, 705},
{118440, 141, 840}, {120600, 201, 600}, {115672, 152, 761},
{116725, 161, 725}, {117067, 167, 701}, {123354, 231, 534},
{129640, 140, 926}, {124483, 281, 443}, {129775, 179, 725},
{125248, 152, 824}, {125433, 231, 543}, {125460, 246, 510},
{125500, 251, 500}, {131242, 311, 422}, {126027, 201, 627},
{132430, 323, 410}, {126846, 261, 486}, {133245, 315, 423},
{134725, 317, 425}, {135828, 588, 231}, {135837, 351, 387},
{136525, 635, 215}, {136948, 146, 938}, {145314, 414, 351},
{146137, 461, 317}, {140350, 401, 350}, {146952, 156, 942},
{152608, 251, 608}, {152685, 585, 261}, {153436, 356, 431},
{150300, 501, 300}, {156240, 651, 240}, {156289, 581, 269},
{156915, 165, 951}, {162976, 176, 926}, {163944, 396, 414},
{172822, 782, 221}, {173250, 750, 231}, {174370, 470, 371},
{180225, 801, 225}, {180297, 897, 201}, {175329, 759, 231},
{182250, 810, 225}, {182650, 281, 650}, {190260, 906, 210},
{192150, 915, 210}, {186624, 864, 216}, {193257, 327, 591},
{193945, 395, 491}, {201852, 252, 801}, {197725, 719, 275},
{205785, 255, 807}, {211896, 216, 981}, {213466, 341, 626},
{215860, 251, 860}, {216733, 671, 323}, {217638, 678, 321},
{218488, 248, 881}, {226498, 269, 842}, {226872, 276, 822},
{229648, 248, 926}, {233896, 338, 692}, {241564, 461, 524},
{245182, 422, 581}, {253750, 350, 725}, {254740, 542, 470},
{251896, 296, 851}, {260338, 323, 806}, {262984, 284, 926},
{263074, 602, 437}, {284598, 489, 582}, {284760, 420, 678},
{286416, 612, 468}, {296320, 926, 320}, {304717, 431, 707},
{312475, 431, 725}, {312975, 321, 975}, {315594, 534, 591},
{315900, 351, 900}, {319059, 351, 909}, {319536, 336, 951},
{326452, 623, 524}, {329346, 342, 963}, {329656, 356, 926},
{336550, 635, 530}, {336960, 360, 936}, {338296, 392, 863},
{346968, 366, 948}, {341653, 641, 533}, {361989, 369, 981},
{362992, 392, 926}, {365638, 686, 533}, {369189, 381, 969},
{368550, 630, 585}, {371893, 383, 971}, {378400, 800, 473},
{378418, 878, 431}, {378450, 870, 435}, {386415, 831, 465},
{384912, 891, 432}, {392566, 593, 662}, {404968, 446, 908},
{416650, 641, 650}, {414895, 491, 845}, {416988, 468, 891},
{428980, 482, 890}, {429664, 464, 926}, {447916, 476, 941},
{456840, 540, 846}, {457600, 704, 650}, {458640, 546, 840},
{475380, 570, 834}, {486720, 624, 780}, {489159, 891, 549},
{489955, 899, 545}, {498550, 845, 590}, {516879, 681, 759},
{529672, 572, 926}, {536539, 563, 953}, {538650, 855, 630},
{559188, 588, 951}, {567648, 657, 864}, {568750, 650, 875},
{629680, 680, 926}, {638950, 650, 983}, {673920, 720, 936},
{679500, 750, 906}, {729688, 788, 926}, {736695, 765, 963},
{738468, 876, 843}, {769792, 776, 992}, {789250, 875, 902},
{789525, 825, 957}, {792585, 927, 855}, {794088, 984, 807},
{809919, 891, 909}, {809964, 894, 906}, {815958, 858, 951},
{829696, 896, 926}, {841995, 891, 945}, {939658, 953, 986}}
Organizando la salida en una tabla:
TableForm[vam,
TableHeadings -> {None, {"vampiro", "colmillo 1", "colmillo 2"}}]
Para aprender más sobre Mathematica ingrese aquí sitio de aprendizaje de Wolfram o en mi website ustamathematica.wixsite.com/basicas
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