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A193447 a(n) = ((p - 2)! + p - 1)/(p*(p - 1)) where p is the n-th prime. 2
3, 3299, 255877, 4807626353, 1040021719579, 100970241446066087, 13409937746820630739862069, 9507270961010432209186683871, 7757618593382991688938927430572972973, 12437732976339904486975781548721278876097561, 18522993694996570934756402022946152638511627907 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,1

COMMENTS

Conjecture: for k >= 7, ((k - 2)! + k - 1)/(k*(k - 1)) is an integer iff k is prime.

Proof follows from Wilson's theorem. - Alois P. Heinz, Aug 07 2011

Note that a(1) = 1 is also an integer. - Jianing Song, Sep 17 2018

LINKS

Table of n, a(n) for n=4..14.

Wikipedia, Wilson's theorem

EXAMPLE

a(4) = (5! + 6)/(7*6) = 126/42 = 3.

a(5) = (9! + 10)/(11*10) = 362890/110 = 3299.

PROG

(PARI) a(n) = my(p=prime(n)); ((p-2)!+p-1)/(p*(p-1)) \\ Jianing Song, Sep 17 2018

CROSSREFS

Cf. A000040, A007619, A066161.

Sequence in context: A281928 A036520 A359130 * A134909 A286215 A259157

Adjacent sequences: A193444 A193445 A193446 * A193448 A193449 A193450

KEYWORD

nonn

AUTHOR

Alzhekeyev Ascar M, Jul 26 2011

EXTENSIONS

Name clarified by Jianing Song, Sep 17 2018

STATUS

approved

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Last modified February 2 04:20 EST 2023. Contains 359997 sequences. (Running on oeis4.)