1,1

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.

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

Obvious variant on A085559.

Sequence in context: A060069 A114950 A003840 this_sequence A167518 A006935 A070833

Adjacent sequences: A122537 A122538 A122539 this_sequence A122541 A122542 A122543

hard,more,nonn,bref

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