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

Author

Eric W. Weisstein, Nov 03 2005

Keywords

• nonn

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

Crossrefs

Cf. A113650.

Programs

Magma

[Fibonacci(n-(KroneckerSymbol(n,5))) mod n^2: n in [1..70]]; // Vincenzo Librandi, May 16 2015

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