A113650 Fibonacci(p-J(p,5)) mod p^2, where p is the n-th prime and J is the Jacobi symbol.

2, 3, 5, 21, 55, 39, 272, 57, 345, 754, 775, 481, 1599, 1677, 752, 1484, 590, 2928, 469, 3905, 4234, 3871, 1743, 445, 3589, 9797, 2266, 2568, 2834, 6780, 1651, 8384, 7946, 16263, 17880, 9060, 6908, 26080, 7348, 22490, 31146, 23711, 17954, 5983

Offset: 1

Author

Eric W. Weisstein, Nov 03 2005

Keywords

• nonn

Comments

A value of 0 indicates a Wall-Sun-Sun prime. No such prime is currently known. - Felix Fröhlich, Jun 07 2014

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. A113649.

Programs

Mathematica

a[n_]:=  ( p=Prime[n];Mod[Fibonacci[p-JacobiSymbol[p, 5]], Power[p, 2]]); Table[a[n], {n,1,50}] (* Javier Rivera Romeu, Mar 03 2022 *)

PARI

a(n)=my(p=prime(n));lift(Mod([1,1;1,0]^(p-kronecker(p,5)),p^2)[1,2]) \\ Charles R Greathouse IV, Oct 31 2011

Sage

def a(n):
    p = Primes().unrank(n-1)
    return fibonacci(p-jacobi_symbol(p, 5))%pow(p, 2)
for n in range(1, 100): print(a(n), end=", ") # Javier Rivera Romeu, Mar 04 2022