A268478 L(p) modulo p^2, where p = prime(n) and L is a Lucas number (A000032).

3, 4, 11, 29, 78, 14, 103, 324, 70, 204, 497, 519, 1477, 1420, 1881, 902, 1476, 3600, 3418, 2202, 5257, 317, 914, 5074, 4269, 9192, 5666, 6421, 7086, 4182, 12193, 3800, 1097, 11677, 299, 22651, 17271, 12063, 18371, 26297, 13784, 10137, 8405, 33583, 11230

Offset

1,1

Comments

Lemma 7 from the Andrejic paper (p. 42): Prime p is a Wall-Sun-Sun prime iff L(p) == 1 (mod p^2). Therefore, a(n) = 1 iff A113650(n) = 0.

Links

Felix Fröhlich, Table of n, a(n) for n = 1..10000

V. Andrejic, On Fibonacci powers, Publikacije Elektrotehnickog fakulteta - serija: matematika, 17 (2006), 38-44.

Formula

a(n) = A180363(n) mod A001248(n). - Michel Marcus, Feb 09 2016

Mathematica

Table[Mod[LucasL[Prime[n]], Prime[n]^2], {n, 60}] (* Vincenzo Librandi, Feb 09 2016 *)

Prog

(PARI) a000032(n) = fibonacci(n+1) + fibonacci(n-1)
a(n) = my(p=prime(n)); lift(Mod(a000032(p), p^2))
(Magma) [Lucas(p) mod p^2: p in PrimesUpTo(250)]; // Bruno Berselli, Feb 09 2016

Crossrefs

Cf. A000032, A000040, A113650, A180363.

Sequence in context: A041231 A042129 A141723 * A180363 A100845 A019169

Adjacent sequences: A268475 A268476 A268477 * A268479 A268480 A268481

Keyword

nonn

Author

Felix Fröhlich, Feb 05 2016

Status

approved