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

1,2

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.

Links

Table of n, a(n) for n=1..24.

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

Prog

(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. */

Crossrefs

Sequence in context: A113720 A034118 A140148 * A037091 A289675 A127303

Adjacent sequences: A117544 A117545 A117546 * A117548 A117549 A117550

Keyword

nonn

Author

T. D. Noe, Mar 29 2006

Extensions

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

Status

approved