

A152217


Primes p == 1 (mod 3) such that ((p1)/3)! == 1 (mod p).


0



3571, 4219, 13669, 25117, 55897, 89269, 102121, 170647, 231019, 246247, 251431
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OFFSET

1,1


COMMENTS

The Wilson theorem states that p is prime if and only if (p1)! = 1 (mod p). If p = 3 (mod 4) then ((p1)/2)! = +/ 1 (mod p).


LINKS

Table of n, a(n) for n=1..11.
J. B. Cosgrave, Jacobi [From Francois Brunault (brunault(AT)gmail.com), Nov 29 2008]
Wikipedia, Wilson's theorem


EXAMPLE

For n = 1 the prime a(1) = 3571 divides 1190!  1.


PROG

(PARI) forprime(p=2, 30000, if(p%3==1 & ((p1)/3)!%p==1, print(p)))


CROSSREFS

Seems to be a subsequence of A002407 and therefore of A003215 (differences of consecutive cubes). See also A058302 and A055939 for the sequences corresponding to ((p1)/2)! = +/ 1 (mod p).
Sequence in context: A204417 A204410 A204409 * A004932 A004952 A004972
Adjacent sequences: A152214 A152215 A152216 * A152218 A152219 A152220


KEYWORD

nonn


AUTHOR

Francois Brunault (brunault(AT)gmail.com), Nov 29 2008, Nov 30 2008


STATUS

approved



