A020896 Positive numbers k such that k = x^5 + y^5 has a solution in nonzero integers x, y.

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

Offset

0,1

Comments

68101 = (15/2)^5 + (17/2)^5 is believed to be the smallest positive integer k which is the sum of two nonzero fifth powers of rational numbers but not the sum of two nonzero fifth powers of integers.

References

J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 99.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..5000

Steven R. Finch, On a Generalized Fermat-Wiles Equation [broken link]

Steven R. Finch, On a Generalized Fermat-Wiles Equation [From the Wayback Machine]

Formula

See Theorem 3.5.6 of J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 99.

Example

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

Steven Finch

Status

approved