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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 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

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