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 A020896 Positive numbers n such that n = x^5 + y^5 has a solution in nonzero integers x, y. 2
 2, 31, 33, 64, 211, 242, 244, 275, 486, 781, 992, 1023, 1025, 1056, 1267, 2048, 2101, 2882, 3093, 3124, 3126, 3157, 3368, 4149, 4651, 6250, 6752, 7533, 7744, 7775, 7777, 7808, 8019, 8800, 9031, 10901, 13682, 15552, 15783, 15961, 16564 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 68101 = (15/2)^5 + (17/2)^5 is believed to be the smallest positive integer n which is the sum of two nonzero fifth powers of rational numbers but not the sum of two nonzero fifth powers of integers. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..5000 J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 99. S. R. Finch, On a Generalized Fermat-Wiles Equation FORMULA See Theorem 3.5.6 of J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 99. EXAMPLE E.g. 31 = 2^5 + (-1)^5. MATHEMATICA Select[Union[Total/@(Select[Tuples[Range[-8, 8], {2}], !MemberQ[#, 0]&]^5)], #>0&]  (* Harvey P. Dale, Apr 03 2011 *) CROSSREFS Cf. A001481, A020897, A003336. Sequence in context: A099189 A247099 A053234 * A042153 A267207 A102630 Adjacent sequences:  A020893 A020894 A020895 * A020897 A020898 A020899 KEYWORD nonn,nice AUTHOR STATUS approved

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Last modified December 12 23:01 EST 2018. Contains 318081 sequences. (Running on oeis4.)