

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 nearWallSunSun prime), where F_k is the kth 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
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OFFSET

1,4


COMMENTS

A value of 0 indicates a WallSunSun 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 FibonacciWieferich and Wolstenholme primes, Math. Comp. 76 (2007), 20872094.
PrimeGrid, WallSunSun Prime Search statistics
PrimeGrid, Welcome to the WallSunSun prime search


PROG

(PARI) forprime(p=2, 10^2, a=fibonacci(pkronecker(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



