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A113495 Lexicographically earliest subsequence of the perfect powers in A025475 such that first differences are an increasing sequence of primes.

%I A113495 #21 Jun 14 2025 23:06:26
%S A113495 1,4,9,16,27,64,125,256,2187,16384,161051,
%T A113495 23945242826029513411849172299223580994042798784118784,
%U A113495 23945249190331908165492143678605499565319109933299901
%N A113495 Lexicographically earliest subsequence of the perfect powers in A025475 such that first differences are an increasing sequence of primes.
%C A113495 Next terms are a(14) = 2^206, a(15) = 590295810335799160457^3, a(16) = 2^754. - _Max Alekseyev_, May 21 2011
%C A113495 Note: if the definition is changed to refer to the perfect powers in A001597, the sequence becomes A137354. - _R. J. Mathar_, Mar 07 2008
%H A113495 Max Alekseyev, <a href="/A113495/b113495.txt">Table of n, a(n) for n = 1..16</a>
%e A113495 a(2) = 4 because 1 + 3 = 4;
%e A113495 a(3) = 9 because 1 + 3 + 5 = 9;
%e A113495 a(4) = 16 because 1 + 3 + 5 + 7 = 16;
%e A113495 a(5) = 27 because 1 + 3 + 5 + 7 + 11 = 27;
%e A113495 a(6) = 64 because 1 + 3 + 5 + 7 + 11 + 37 = 64;
%e A113495 a(7) = 125 because 1 + 3 + 5 + 7 + 11 + 37 + 61 = 125;
%e A113495 a(8) = 256 because 1 + 3 + 5 + 7 + 11 + 37 + 61 + 131 = 256.
%Y A113495 Cf. A113759.
%K A113495 nonn
%O A113495 1,2
%A A113495 _Giovanni Teofilatto_, Jan 10 2006
%E A113495 3 more terms from _R. J. Mathar_, Mar 07 2008
%E A113495 a(12) from _Donovan Johnson_, Aug 09 2010
%E A113495 a(13)-a(16) from _Max Alekseyev_, May 21 2011