%I A122540
%S A122540 2,137633,409698593
%N A122540 Primes that can be written in n ways as the sum of three fourth powers.
%C A122540 If you replace 'prime' with 'odd number', the sequence is 17, 2673, 16196193, 
               155129315313, ... Next term is at least 3000^4.
%C A122540 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.
%e A122540 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
%e A122540 a(3)=409698593; 128^4+109^4+18^4 = 129^4+94^4+86^4 = 142^4+42^4+1
%Y A122540 Obvious variant on A085559.
%Y A122540 Sequence in context: A060069 A114950 A003840 this_sequence A167518 A006935 
               A070833
%Y A122540 Adjacent sequences: A122537 A122538 A122539 this_sequence A122541 A122542 
               A122543
%K A122540 hard,more,nonn,bref
%O A122540 1,1
%A A122540 Thomas Womack (tom(AT)womack.net), Sep 19 2006