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A003336 Numbers that are the sum of 2 nonzero 4th powers. 34
2, 17, 32, 82, 97, 162, 257, 272, 337, 512, 626, 641, 706, 881, 1250, 1297, 1312, 1377, 1552, 1921, 2402, 2417, 2482, 2592, 2657, 3026, 3697, 4097, 4112, 4177, 4352, 4721, 4802, 5392, 6497, 6562, 6577, 6642, 6817, 7186, 7857, 8192, 8962, 10001, 10016 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n such that n = x^4 + y^4 has a solution in positive integers x, y.

There are no squares in this sequence. - Altug Alkan, Apr 08 2016

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

A. Bremner and P. Morton, A new characterization of the integer 5906, Manuscripta Math. 44 (1983) 187-229; Math. Rev. 84i:10016.

S. R. Finch, On a generalized Fermat-Wiles equation [broken link]

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

Eric Weisstein's World of Mathematics, Biquadratic Number

MATHEMATICA

nn=12; Select[Union[Plus@@@(Tuples[Range[nn], {2}]^4)], # <= nn^4&] (* Harvey P. Dale, Dec 29 2010 *)

Select[Range@ 11000, Length[PowersRepresentations[#, 2, 4] /. {0, _} -> Nothing] > 0 &] (* Michael De Vlieger, Apr 08 2016 *)

PROG

(PARI) list(lim)=my(v=List(2)); for(x=1, lim^.25, for(y=1, min((lim-x^4)^.25, x), listput(v, x^4+y^4))); vecsort(Vec(v), , 8) \\ Charles R Greathouse IV, Apr 24 2012

(PARI) T=thueinit('x^4+1, 1);

is(n)=#thue(T, n)>0 && !issquare(n) \\ Charles R Greathouse IV, Feb 26 2017

CROSSREFS

5906 is the first term in A060387 but not in this sequence. Cf. A020897.

Cf. A088687 (2 distinct 4th powers)

Sequence in context: A162622 A078164 A060387 * A212740 A212742 A178145

Adjacent sequences:  A003333 A003334 A003335 * A003337 A003338 A003339

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 14 17:43 EDT 2019. Contains 328022 sequences. (Running on oeis4.)