A096739 Numbers k such that k^4 can be written as a sum of four distinct positive 4th powers.

353, 651, 706, 1059, 1302, 1412, 1765, 1953, 2118, 2471, 2487, 2501, 2604, 2824, 2829, 3177, 3255, 3530, 3723, 3883, 3906, 3973, 4236, 4267, 4333, 4449, 4557, 4589, 4942, 4949, 4974, 5002, 5208, 5281, 5295, 5463, 5491, 5543, 5648, 5658, 5729, 5859

Offset

1,1

Comments

From David Wasserman, Nov 16 2007: (Start)

Every multiple of a term is a term.

Is this sequence the same as A003294? (End)

References

D. Wells, Curious and interesting numbers, Penguin Books, p. 139.

Links

Table of n, a(n) for n=1..42.

K. Rose and S. Brudno, More about four biquadrates equal one biquadrate, Math. Comp., 27 (1973), 491-494.

Eric Weisstein's World of Mathematics, Diophantine Equation 4th Powers.

Example

Example solutions:
   353^4 =   30^4 +  120^4 +  272^4 +  315^4;
   706^4 =   60^4 +  240^4 +  544^4 +  630^4;
  1059^4 =   90^4 +  360^4 +  816^4 +  945^4;
  1302^4 =  480^4 +  680^4 +  860^4 + 1198^4;
  1412^4 =  120^4 +  480^4 + 1088^4 + 1260^4;
  3723^4 = 2270^4 + 2345^4 + 2460^4 + 3152^4.

Crossrefs

Cf. A003294, A176197.

Sequence in context: A058375 A059635 A003294 * A039664 A054825 A304385

Adjacent sequences: A096736 A096737 A096738 * A096740 A096741 A096742

Keyword

nonn

Author

Lekraj Beedassy, May 30 2002

Extensions

Corrected by Bo Asklund (boa(AT)mensa.se), Nov 05 2004

Corrected and extended by David Wasserman, Nov 16 2007

Status

approved