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
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
KEYWORD
nonn
AUTHOR
Alzhekeyev Ascar M, Jul 26 2011
EXTENSIONS
Name clarified by Jianing Song, Sep 17 2018
STATUS
approved