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

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

Keyword

nonn,more

Author

Daniel Suteu, Apr 03 2018

Extensions

a(21) from Robert G. Wilson v, Apr 05 2018

a(22) from Vaclav Kotesovec, Apr 06 2018

a(23) from Giovanni Resta, Jun 24 2018

Status

approved