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A244801 Smallest m such that for the prime p = prime(n) the congruence F_(p-(p/5)) == mp (mod p^2) holds (i.e. smallest m such that prime(n) is a near-Wall-Sun-Sun prime), where F_k is the k-th Fibonacci number and (p/5) is the Legendre symbol. 8
1, 1, 1, 3, 5, 3, 16, 3, 15, 26, 25, 13, 39, 39, 16, 28, 10, 48, 7, 55, 58, 49, 21, 5, 37, 97, 22, 24, 26, 60, 13, 64, 58, 117, 120, 60, 44, 160, 44, 130, 174, 131, 94, 31, 141, 5, 112, 3, 154, 18, 29, 5, 182, 250, 2, 105 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A value of 0 indicates a Wall-Sun-Sun prime. No such prime is known and if one exists it is > 4*10^16 (Cf. PrimeGrid WSS statistics).

LINKS

Felix Fröhlich, Table of n, a(n) for n = 1..291043

F. G. Dorais and D. Klyve, A Wieferich Prime Search up to 6.7 x 10^15, J. Integer Seq. Volume 14, Issue 9 (2011).

R. J. McIntosh and E. L. Roettger, A search for Fibonacci-Wieferich and Wolstenholme primes, Math. Comp. 76 (2007), 2087-2094.

PrimeGrid, Wall-Sun-Sun Prime Search statistics

PrimeGrid, Welcome to the Wall-Sun-Sun prime search

PROG

(PARI) forprime(p=2, 10^2, a=fibonacci(p-kronecker(p, 5))%p^2; a=a/p; print1(a, ", "))

CROSSREFS

Cf. A000045, A113650, A195988.

Sequence in context: A121278 A023587 A172003 * A002586 A258811 A066845

Adjacent sequences:  A244798 A244799 A244800 * A244802 A244803 A244804

KEYWORD

nonn

AUTHOR

Felix Fröhlich, Jul 06 2014

STATUS

approved

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Last modified April 1 03:08 EDT 2020. Contains 333155 sequences. (Running on oeis4.)