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

1,1

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

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 *)

Prog

(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

Crossrefs

Cf. A113649.

Sequence in context: A065398 A084838 A051694 * A259376 A060321 A351989

Adjacent sequences: A113647 A113648 A113649 * A113651 A113652 A113653

Keyword

nonn

Author

Eric W. Weisstein, Nov 03 2005

Status

approved