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Search: id:A152217
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| A152217 |
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Primes p == 1 (mod 3) such that ((p-1)/3)! == 1 (mod p). |
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+0
1
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| 3571, 4219, 13669, 25117, 55897, 89269, 102121, 170647, 231019, 246247, 251431
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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).
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LINKS
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J. B. Cosgrave, Jacobi [From Francois Brunault (brunault(AT)gmail.com), Nov 29 2008]
Wikipedia, Wilson's theorem
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EXAMPLE
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For n = 1 the prime a(1) = 3571 divides 1190! - 1.
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PROGRAM
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(PARI) forprime(p=2, 30000, if(p%3==1 & ((p-1)/3)!%p==1, print(p)))
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CROSSREFS
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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).
Sequence in context: A104207 A107646 A071144 this_sequence A004932 A004952 A004972
Adjacent sequences: A152214 A152215 A152216 this_sequence A152218 A152219 A152220
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KEYWORD
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nonn
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AUTHOR
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Francois Brunault (brunault(AT)gmail.com), Nov 29 2008, Nov 30 2008
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