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%I A255351 #30 Oct 24 2023 03:22:44
%S A255351 158,239,292,316,474,478,502,542,584,631,632,717,790,876,948,956,1004,
%T A255351 1084,1106,1168,1195,1203,1262,1264,1381,1422,1434,1460,1506,1580,
%U A255351 1626,1673,1738,1752,1893,1896,1912
%N A255351 Values of b = max {a,b,c,d} for solutions to a^4 + b^4 = c^4 + d^4, a < c < d < b, ordered by size of b.
%C A255351 See A018786 for the values of a^4 + b^4 = c^4 + d^4, and A255352 for the list of the full quadruples (a,b,c,d). See there for further comments, motivation and references.
%C A255351 The values of b listed here allow one to reproduce the full solutions (a,b,c,d) with not too much effort, cf. the inner loops of the PARI code.
%H A255351 Mia Muessig, <a href="/A255351/b255351.txt">Table of n, a(n) for n = 1..30000</a>
%H A255351 Mia Muessig, <a href="https://github.com/PhoenixSmaug/taxicab-numbers">Julia code for finding general taxicab numbers</a>
%e A255351 The quadruples [a,b,c,d] are, listed in order of increasing b = max{a,b,c,d}):
%e A255351 [59, 158, 133, 134], [7, 239, 157, 227], [193, 292, 256, 257], [118, 316, 266, 268], [177, 474, 399, 402], [14, 478, 314, 454], [271, 502, 298, 497], [103, 542, 359, 514], [386, 584, 512, 514], [222, 631, 503, 558], [236, 632, 532, 536], [21, 717, 471, 681], [295, 790, 665, 670], [579, 876, 768, 771], [354, 948, 798, 804], [28, 956, 628, 908], ...
%o A255351 (PARI) {n=4;for(b=1,1999,for(a=1,b,t=a^n+b^n;for(c=a+1,sqrtn(t\2,n),ispower(t-c^n,n)||next;print1(b",");next(3))))}
%Y A255351 Cf. A018786, A255352.
%K A255351 nonn
%O A255351 1,1
%A A255351 _M. F. Hasler_, Feb 21 2015

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