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a(n) = greatest integer p such that n^p + (n+1)^p + (n+2)^p > (n+3)^p.
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%I #2 Mar 30 2012 18:57:06

%S 0,1,2,2,3,4,4,5,6,6,7,7,8,9,9,10,10,11,12,12,13,14,14,15,15,16,17,17,

%T 18,18,19,20,20,21,21,22,23,23,24,24,25,26,26,27,28,28,29,29,30,31,31,

%U 32,32,33,34,34,35,35,36,37,37,38,39,39,40,40,41,42,42,43,43,44,45,45

%N a(n) = greatest integer p such that n^p + (n+1)^p + (n+2)^p > (n+3)^p.

%C These occur once: 0,1,3,5,8,11,13,16,19,22,...

%e a(6) = 4: 6^4 + 7^4 + 8^4 > 9^4,

%e but 6^5 + 7^5 + 8^5 < 9^5.

%Y Cf. A111660.

%K nonn

%O 0,3

%A _Clark Kimberling_, Sep 03 2005