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A020896 Positive numbers k such that k = 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 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,changed

AUTHOR

Steven Finch

STATUS

approved

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Last modified February 26 03:10 EST 2021. Contains 341619 sequences. (Running on oeis4.)