A301373 - OEIS

A301373

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

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

The associated primes are A300559(a(n)) = A180119(a(n))+1 = A001286(a(n)+1)+1. - M. F. Hasler, Apr 10 2018

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

Table of n, a(n) for n=1..23.

Maheswara Rao Valluri, Primes of the form p = 1 + n! Sum n, for some n ∈ N*, arXiv:1803.11461 [math.GM], 2018.

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

Cf. A090703, A300559, A180119, A001286.

See A302859 for the actual primes.

Sequence in context: A191890 A247814 A082918 * A354581 A193096 A353744

Adjacent sequences: A301370 A301371 A301372 * A301374 A301375 A301376