

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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 * A193096 A309129 A307345
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



