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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
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
See A302859 for the actual primes.
Sequence in context: A191890 A247814 A082918 * A354581 A193096 A353744
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

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Last modified July 19 01:31 EDT 2024. Contains 374388 sequences. (Running on oeis4.)