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

1, 4, 9, 16, 27, 64, 125, 256, 2187, 16384, 161051, 23945242826029513411849172299223580994042798784118784, 23945249190331908165492143678605499565319109933299901

Offset: 1

Author

Giovanni Teofilatto, Jan 10 2006

Keywords

• nonn

Comments

Next terms are a(14) = 2^206, a(15) = 590295810335799160457^3, a(16) = 2^754. - Max Alekseyev, May 21 2011

Note: if the definition is changed to refer to the perfect powers in A001597, the sequence becomes A137354. - R. J. Mathar, Mar 07 2008

Examples

			a(2) = 4 because 1 + 3 = 4;
a(3) = 9 because 1 + 3 + 5 = 9;
a(4) = 16 because 1 + 3 + 5 + 7 = 16;
a(5) = 27 because 1 + 3 + 5 + 7 + 11 = 27;
a(6) = 64 because 1 + 3 + 5 + 7 + 11 + 37 = 64;
a(7) = 125 because 1 + 3 + 5 + 7 + 11 + 37 + 61 = 125;
a(8) = 256 because 1 + 3 + 5 + 7 + 11 + 37 + 61 + 131 = 256.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..16

Crossrefs

Cf. A113759.

Extensions

3 more terms from R. J. Mathar, Mar 07 2008

a(12) from Donovan Johnson, Aug 09 2010

a(13)-a(16) from Max Alekseyev, May 21 2011