A113649 Fibonacci(n-J(n,5)) mod n^2, where J is the Jacobi symbol.

0, 2, 3, 2, 5, 5, 21, 34, 21, 55, 55, 89, 39, 37, 160, 98, 272, 293, 57, 365, 150, 101, 345, 433, 25, 665, 696, 709, 754, 440, 775, 994, 883, 1090, 765, 1241, 481, 230, 1511, 1355, 1599, 257, 1677, 805, 20, 1382, 752, 289, 2275, 1525, 1414, 821, 1484

Offset

1,2

Comments

a(n) == 0 for n > 1 iff either n is a Wall-Sun-Sun prime (when n is prime) or a 'Wall-Sun-Sun pseudoprime' (when n is composite). The numbers meeting the second criterion are those composites where the congruence in A241505 is satisfied modulo n^2. No members are known from either of those two sets of numbers. - Felix Fröhlich, May 15 2015

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Wall-Sun-Sun Prime

Prog

(PARI) a(n)=lift(Mod([1, 1; 1, 0]^(n-kronecker(n, 5)), n^2)[1, 2]) \\ Charles R Greathouse IV, Oct 31 2011
(PARI) a(n) = fibonacci(n-kronecker(n, 5)) % n^2 \\ Jeppe Stig Nielsen, Jul 22 2014
(Magma) [Fibonacci(n-(KroneckerSymbol(n, 5))) mod n^2: n in [1..70]]; // Vincenzo Librandi, May 16 2015

Crossrefs

Cf. A113650.

Sequence in context: A239327 A021047 A249492 * A307864 A066119 A003970

Adjacent sequences: A113646 A113647 A113648 * A113650 A113651 A113652

Keyword

nonn

Author

Eric W. Weisstein, Nov 03 2005

Status

approved