%I #19 Feb 27 2018 01:11:47

%S 1,4,9,16,27,64,125,256,2187,16384,161051,

%T 23945242826029513411849172299223580994042798784118784,

%U 23945249190331908165492143678605499565319109933299901

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

%C Next terms are a(14) = 2^206, a(15) = 590295810335799160457^3, a(16) = 2^754. - _Max Alekseyev_, May 21 2011

%C 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 Max Alekseyev, <a href="/A113495/b113495.txt">Table of n, a(n) for n = 1..16</a>

%e a(2) = 4 because 1 + 3 = 4;

%e a(3) = 9 because 1 + 3 + 5 = 9;

%e a(4) = 16 because 1 + 3 + 5 + 7 = 16;

%e a(5) = 27 because 1 + 3 + 5 + 7 + 11 = 27;

%e a(6) = 64 because 1 + 3 + 5 + 7 + 11 + 37 = 64;

%e a(7) = 125 because 1 + 3 + 5 + 7 + 11 + 37 + 61 = 125;

%e a(8) = 256 because 1 + 3 + 5 + 7 + 11 + 37 + 61 + 131 = 256.

%Y Cf. A113759.

%K nonn

%O 1,2

%A _Giovanni Teofilatto_, Jan 10 2006

%E 3 more terms from _R. J. Mathar_, Mar 07 2008

%E a(12) from _Donovan Johnson_, Aug 09 2010

%E a(13)-a(16) from _Max Alekseyev_, May 21 2011