1,1

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.

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.

Mia Muessig, Table of n, a(n) for n = 1..30000

Mia Muessig, Julia code for finding general taxicab numbers

The quadruples [a,b,c,d] are, listed in order of increasing b = max{a,b,c,d}:

[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], ...

(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))))}

Cf. A018786, A255352.

Sequence in context: A045245 A053235 A352349 * A088728 A258960 A072555

Adjacent sequences: A255348 A255349 A255350 * A255352 A255353 A255354

M. F. Hasler, Feb 21 2015

approved