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

1,2

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

Links

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

Example

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.

Crossrefs

Cf. A113759.

Sequence in context: A132074 A283549 A137354 * A110997 A001640 A161328

Adjacent sequences: A113492 A113493 A113494 * A113496 A113497 A113498

Keyword

nonn

Author

Giovanni Teofilatto, Jan 10 2006

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

Status

approved