A122540 Primes that can be written in n ways as the sum of three fourth powers.

2, 137633, 409698593

Offset

1,1

Comments

If you replace 'prime' with 'odd number', the sequence is 17, 2673, 16196193, 155129315313, ... Next term is at least 3000^4.

The restriction to primes is quite severe and to odd numbers reasonably so; otherwise x^4+y^4+(x+y)^4=2(x^2+xy+y^2)^2 gives very many examples of the form 2k^2.

Links

Table of n, a(n) for n=1..3.

Example

a(2)=137633; 8^4+13^4+18^4 = 9^4+16^4+16^4 and this is the smallest prime N for which this holds
a(3)=409698593; 128^4+109^4+18^4 = 129^4+94^4+86^4 = 142^4+42^4+1

Crossrefs

Obvious variant on A085559.

Sequence in context: A170995 A319022 A003840 * A324438 A167518 A178168

Adjacent sequences: A122537 A122538 A122539 * A122541 A122542 A122543

Keyword

hard,more,nonn,bref

Author

Thomas Womack (tom(AT)womack.net), Sep 19 2006

Status

approved