clearvars,clc
S=2;
i=1;
while i<=599
n=S(i);
if n<1000000
S(end+1)=(n+5)^2;
sr=round(sqrt(n));
if sr^2==n
S(end+1)=sr;
S=unique(S,'stable');
i=find(S==sr);
else
i=i+1;
end
else
i=i+1;
end
end
S=unique(S);
fprintf('%4d, %4d, %4d, %4d, %4d, %4d, %4d, %4d, %4d,
',S)
2, 7, 12, 17, 22, 27, 32, 37, 42,
47, 49, 52, 57, 62, 67, 72, 77, 82,
87, 92, 97, 102, 107, 112, 117, 122, 127,
132, 137, 142, 144, 147, 152, 157, 162, 167,
172, 177, 182, 187, 192, 197, 202, 207, 212,
217, 222, 227, 232, 237, 242, 247, 252, 257,
262, 267, 272, 277, 282, 287, 289, 292, 297,
302, 307, 312, 317, 322, 327, 332, 337, 342,
347, 352, 357, 362, 367, 372, 377, 382, 387,
392, 397, 402, 407, 412, 417, 422, 427, 432,
437, 442, 447, 452, 457, 462, 467, 472, 477,
482, 484, 487, 492, 497, 502, 507, 512, 517,
522, 527, 532, 537, 542, 547, 552, 557, 562,
567, 572, 577, 582, 587, 592, 597, 602, 607,
612, 617, 622, 627, 632, 637, 642, 647, 652,
657, 662, 667, 672, 677, 682, 687, 692, 697,
702, 707, 712, 717, 722, 727, 729, 732, 737,
742, 747, 752, 757, 762, 767, 772, 777, 782,
787, 792, 797, 802, 807, 812, 817, 822, 827,
832, 837, 842, 847, 852, 857, 862, 867, 872,
877, 882, 887, 892, 897, 902, 907, 912, 917,
922, 927, 932, 937, 942, 947, 952, 957, 962,
967, 972, 977, 982, 987, 992, 997, 1024, 1369,
1764, 2209, 2704, 2916, 3249, 3844, 4489, 5184, 5929,
6724, 7569, 8464, 9409, 10404, 11449, 12544, 13689, 14884,
16129, 17424, 18769, 20164, 21609, 22201, 23104, 24649, 26244,
27889, 29584, 31329, 33124, 34969, 36864, 38809, 40804, 42849,
44944, 47089, 49284, 51529, 53824, 56169, 58564, 61009, 63504,
66049, 68644, 71289, 73984, 76729, 79524, 82369, 85264, 86436,
88209, 91204, 94249, 97344, 100489, 103684, 106929, 110224, 113569,
116964, 120409, 123904, 127449, 131044, 134689, 138384, 142129, 145924,
149769, 153664, 157609, 161604, 165649, 169744, 173889, 178084, 182329,
186624, 190969, 195364, 199809, 204304, 208849, 213444, 218089, 222784,
227529, 232324, 237169, 239121, 242064, 247009, 252004, 257049, 262144,
267289, 272484, 277729, 283024, 288369, 293764, 299209, 304704, 310249,
315844, 321489, 327184, 332929, 338724, 344569, 350464, 356409, 362404,
368449, 374544, 380689, 386884, 393129, 399424, 405769, 412164, 418609,
425104, 431649, 438244, 444889, 451584, 458329, 465124, 471969, 478864,
485809, 492804, 499849, 506944, 514089, 521284, 528529, 535824, 538756,
543169, 550564, 558009, 565504, 573049, 580644, 588289, 595984, 603729,
611524, 619369, 627264, 635209, 643204, 651249, 659344, 667489, 675684,
683929, 692224, 700569, 708964, 717409, 725904, 734449, 743044, 751689,
760384, 769129, 777924, 786769, 795664, 804609, 813604, 822649, 831744,
840889, 850084, 859329, 868624, 877969, 887364, 896809, 906304, 915849,
925444, 935089, 944784, 954529, 964324, 974169, 984064, 994009, 1004004,
1058841, 1887876, 3129361, 4901796, 7338681, 10588516, 14814801, 20196036, 26925721,
35212356, 45279441, 57365476, 71723961, 88623396, 108347281, 131194116, 157477401, 187525636,
221682321, 260305956, 303770041, 352463076, 406788561, 467164996, 534025881, 607819716, 689010001,
778075236, 875508921, 981819556, 1097530641, 1223180676, 1359323161, 1506526596, 1665374481, 1836465316,
2020412601, 2217844836, 2429405521, 2655753156, 2897561241, 3155518276, 3430327761, 3722708196, 4033393081,
4363130916, 4712685201, 5082834436, 5474372121, 5888106756, 6324861841, 6785475876, 7270802361, 7781709796,
8319081681, 8883816516, 9476827801, 10099044036, 10751408721, 11434880356, 12150432441, 12899053476, 13681746961,
14499531396, 15353440281, 16244522116, 17173840401, 18142473636, 19151515321, 20202073956, 21295273041, 22432251076,
23614161561, 24842172996, 26117468881, 27441247716, 28814723001, 30239123236, 31715691921, 33245687556, 34830383641,
36471068676, 38169046161, 39925634596, 41742167481, 43619993316, 45560475601, 47564992836, 49634938521, 51771721156,
53976764241, 56251506276, 58597400761, 61015916196, 63508536081, 66076758916, 68722098201, 71446082436, 74250255121,
77136174756, 80105414841, 83159563876, 86300225361, 89529017796, 92847574681, 96257544516, 99760590801, 103358392036,
107052641721, 110845048356, 114737335441, 118731241476, 122828519961, 127030939396, 131340283281, 135758350116, 140286953401,
144927921636, 149683098321, 154554341956, 159543526041, 164652539076, 169883284561, 175237680996, 180717661881, 186325175716,
192062186001, 197930671236, 203932624921, 210070055556, 216344986641, 222759456676, 229315519161, 236015242596, 242860710481,
249854021316, 256997288601, 264292640836, 271742221521, 279348189156, 287112717241, 295037994276, 303126223761, 311379624196,
319800429081, 328390886916, 337153261201, 346089830436, 355202888121, 364494742756, 373967717841, 383624151876, 393466398361,
403496825796, 413717817681, 424131772516, 434741103801, 445548240036, 456555624721, 467765716356, 479180988441, 490803929476,
502637042961, 514682847396, 526943876281, 539422678116, 552121816401, 565043869636, 578191431321, 591567109956, 605173529041,
619013327076, 633089157561, 647403688996, 661959604881, 676759603716, 691806399001, 707102719236, 722651307921, 738454923556,
754516339641, 770838344676, 787423742161, 804275350596, 821396003481, 838788549316, 856455851601, 874400788836, 892626254521,
911135157156, 929930420241, 949014982276, 968391796761, 988063832196, >>
There's a flaw in the program, that it isn't infinite.
Note that 49 is on the list, but not 54. But 49+5 = 54 so that 54^2 = 2916 is on the list. That means sqrt(2916) = 54 should be on the list, but we never get to examining it due to the limit on i.
But we do see the integers ending in 2 and 7 are apparent on the list, and eventually those ending in 4 and 9 and 1 and 6 appear.
Absent on this list are numbers ending in 3 and 8 and in 0 and 5. Is this significant, or an artifact of the flaw in the program?
Edited on February 18, 2024, 10:23 am
|
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Posted by Charlie
on 2024-02-18 10:22:37 |
flawed program, but some ideas
