

A301373


Numbers k such that (k+1)!*k/2 + 1 is prime.


3



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 19, 24, 251, 374, 953, 1104, 1507, 3390, 4443, 5762
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OFFSET

1,2


COMMENTS

Looking for primes of the form p(n) = 1 + n! f(n) with a simple polynomial function f, it appears that the choice f(n) = n(n+1)/2 = A000217 is one of the most successful choices for getting a maximum of primes for n = 1..20.  M. F. Hasler, Apr 14 2018
The PFGW program has been used to certify all the terms up to a(23), using a deterministic test which exploits the factorization of a(n)  1.  Giovanni Resta, Jun 24 2018


LINKS



MATHEMATICA

Do[ If[ PrimeQ[n(n +1)!/2 +1], Print@ n], {n, 4000}] (* Robert G. Wilson v, Apr 05 2018 *)


PROG

(PARI) isok(k) = ispseudoprime((k+1)! * k / 2 + 1);


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



