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

Author

Felix Fröhlich, Feb 05 2016

Keywords

• nonn

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.

Crossrefs

Cf. A000032, A000040, A113650, A180363.

Programs

Magma

[Lucas(p) mod p^2: p in PrimesUpTo(250)]; // Bruno Berselli, Feb 09 2016

Mathematica

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

PARI

a000032(n) = fibonacci(n+1) + fibonacci(n-1)
a(n) = my(p=prime(n)); lift(Mod(a000032(p), p^2))

Formula

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