Search: id:A152217
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%I A152217
%S A152217 3571,4219,13669,25117,55897,89269,102121,170647,231019,246247,251431
%N A152217 Primes p == 1 (mod 3) such that ((p-1)/3)! == 1 (mod p).
%C A152217 The Wilson theorem states that p is prime if and only if (p-1)! = -1 
               (mod p). If p = 3 (mod 4) then ((p-1)/2)! = +/- 1 (mod p).
%H A152217 J. B. Cosgrave, <a href="http://staff.spd.dcu.ie/johnbcos/jacobi.htm">
               Jacobi</a> [From Francois Brunault (brunault(AT)gmail.com), Nov 29 
               2008]
%H A152217 Wikipedia, <a href="http://en.wikipedia.org/wiki/Wilson's_theorem">Wilson's 
               theorem</a>
%e A152217 For n = 1 the prime a(1) = 3571 divides 1190! - 1.
%o A152217 (PARI) forprime(p=2,30000,if(p%3==1 & ((p-1)/3)!%p==1,print(p)))
%Y A152217 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 ((p-1)/2)! = +/- 1 (mod p).
%Y A152217 Sequence in context: A104207 A107646 A071144 this_sequence A004932 A004952 
               A004972
%Y A152217 Adjacent sequences: A152214 A152215 A152216 this_sequence A152218 A152219 
               A152220
%K A152217 nonn
%O A152217 1,1
%A A152217 Francois Brunault (brunault(AT)gmail.com), Nov 29 2008, Nov 30 2008

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