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%I #1 Sep 29 2006 03:00:00
%S 2,137633,409698593
%N Primes that can be written in n ways as the sum of three fourth powers.
%C If you replace 'prime' with 'odd number', the sequence is 17, 2673, 16196193, 155129315313, ... Next term is at least 3000^4.
%C 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 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 a(3)=409698593; 128^4+109^4+18^4 = 129^4+94^4+86^4 = 142^4+42^4+1
%Y Obvious variant on A085559.
%K hard,more,nonn,bref
%O 1,1
%A Thomas Womack (tom(AT)womack.net), Sep 19 2006
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