A117547 Numbers n such that 2*n^2+1 is a perfect power.

0, 2, 11, 12, 70, 408, 2378, 13860, 80782, 470832, 2744210, 15994428, 93222358, 543339720, 3166815962, 18457556052, 107578520350, 627013566048, 3654502875938, 21300003689580, 124145519261542, 723573111879672, 4217293152016490, 24580185800219268

Offset: 1

Author

T. D. Noe, Mar 29 2006

Keywords

• nonn

Comments

The value of y in the solution of the Diophantine equation x^a - 2*y^b = 1. All solutions have b=2. Sequence A075114 gives n^2. The only known solution for a>2 is y=11. See A075114 for more details.

Programs

PARI

Vec(x^2*(2-x-52*x^2+9*x^3)/ (1-6*x+x^2) + O(x^66))
/* Joerg Arndt, Apr 28 2012, using Colin Barker's g.f. */

Formula

Conjecture: a(n) = 6*a(n-1) - a(n-2) for n>5; g.f.: x^2*(2-x-52*x^2+9*x^3)/ (1-6*x+x^2). - Colin Barker, Apr 28 2012

Extensions

More terms from T. D. Noe, Nov 19 2006