OFFSET
1,1
COMMENTS
Sequence gives solutions k to the Diophantine equation A^4 + B^4 + C^4 + D^4 = k^4.
Is this sequence the same as A096739? - David Wasserman, Nov 16 2007
A138760 (numbers k such that k^4 is a sum of 4th powers of four nonzero integers whose sum is k) is a subsequence. - Jonathan Sondow, Apr 06 2008
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. Wells, Curious and interesting numbers, Penguin Books, p. 139.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..4870 (using Wroblewski's results)
Simcha Brudno, A further example of A^4 + B^4 + C^4 + D^4 = E^4, Proc. Camb. Phil. Soc. 60 (1964) 1027-1028.
Lee W. Jacobi and Daniel J. Madden, On a^4 + b^4 + c^4 + d^4 = (a+b+c+d)^4, Amer. Math. Monthly 115 (2008) 220-236.
Kermit Rose and Simcha Brudno, More about four biquadrates equal one biquadrate, Math. Comp., 27 (1973), 491-494.
Eric Weisstein's World of Mathematics, Diophantine Equation 4th Powers.
Jaroslaw Wroblewski, Exhaustive list of 1009 solutions to (4,1,4) below 222,000.
EXAMPLE
353^4 = 30^4 + 120^4 + 272^4 + 315^4.
651^4 = 240^4 + 340^4 + 430^4 + 599^4.
2487^4 = 435^4 + 710^4 + 1384^4 + 2420^4.
2501^4 = 1130^4 + 1190^4 + 1432^4 + 2365^4.
2829^4 = 850^4 + 1010^4 + 1546^4 + 2745^4.
MATHEMATICA
fourthPowerSums = {};
Do[a4 = a^4; Do[b4 = b^4; Do[c4 = c^4; Do[d4 = d^4; e4 = a4 + b4 + c4 + d4; e = Sqrt[Sqrt[e4]]; If[IntegerQ[e], AppendTo[fourthPowerSums, e]], {d, c + 1, 9000}], {c, b + 1, 6000}], {b, a + 1, 5000}], {a, 30, 3000}];
Union @ fourthPowerSums (* Vladimir Joseph Stephan Orlovsky, May 19 2010 *)
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
Corrected and extended by Don Reble, Jul 07 2007
More terms from David Wasserman, Nov 16 2007
Definition clarified by Jonathan Sondow, Apr 06 2008
STATUS
approved