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A163079 Primes p such that p$ + 1 is also prime. Here '$' denotes the swinging factorial function (A056040). 4
2, 3, 5, 31, 67, 139, 631, 9743, 16253, 17977, 27901, 37589 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) are the primes in A163077.

LINKS

Table of n, a(n) for n=1..12.

Peter Luschny, Die schwingende Fakult├Ąt und Orbitalsysteme, August 2011.

Peter Luschny, Swinging Primes.

EXAMPLE

5 is prime and 5$ + 1 = 30 + 1 = 31 is prime, so 5 is in the sequence.

MAPLE

a := proc(n) select(isprime, select(k -> isprime(A056040(k)+1), [$0..n])) end:

MATHEMATICA

f[n_] := 2^(n - Mod[n, 2])*Product[k^((-1)^(k + 1)), {k, n}]; p = 2; lst = {}; While[p < 38000, a = f@p + 1; If[ PrimeQ@a, AppendTo[ lst, p]; Print@p]; p = NextPrime@p]; lst (* Robert G. Wilson v, Aug 08 2010 *)

PROG

(PARI) is(k) = isprime(k) && ispseudoprime(1+k!/(k\2)!^2); \\ Jinyuan Wang, Mar 22 2020

CROSSREFS

Cf. A002981, A062363, A093804, A163077.

Cf. A056040. - Robert G. Wilson v, Aug 09 2010

Sequence in context: A265807 A106308 A036797 * A109845 A241722 A276043

Adjacent sequences:  A163076 A163077 A163078 * A163080 A163081 A163082

KEYWORD

nonn,more

AUTHOR

Peter Luschny, Jul 21 2009

EXTENSIONS

a(8)-a(12) from Robert G. Wilson v, Aug 08 2010

STATUS

approved

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Last modified October 28 06:26 EDT 2020. Contains 338048 sequences. (Running on oeis4.)