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A163079
Primes p such that p$ + 1 is also prime. Here '$' denotes the swinging factorial function (A056040).
4
2, 3, 5, 31, 67, 139, 631, 9743, 16253, 17977, 27901, 37589
OFFSET
1,1
COMMENTS
a(n) are the primes in A163077.
EXAMPLE
5 is prime and 5$ + 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. A056040. - Robert G. Wilson v, Aug 09 2010
Sequence in context: A265807 A106308 A036797 * A109845 A241722 A276043
KEYWORD
nonn,more
AUTHOR
Peter Luschny, Jul 21 2009
EXTENSIONS
a(8)-a(12) from Robert G. Wilson v, Aug 08 2010
STATUS
approved