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A163079
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Primes p such that p$ + 1 is also prime. Here '$' denotes the swinging factorial function (A056040).
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4
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2, 3, 5, 31, 67, 139, 631, 9743, 16253, 17977, 27901, 37589
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OFFSET
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1,1
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COMMENTS
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a(n) are the primes in A163077.
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LINKS
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Table of n, a(n) for n=1..12.
Peter Luschny, Die schwingende Fakultät und Orbitalsysteme, August 2011.
Peter Luschny, Swinging Primes.
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EXAMPLE
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5 is prime and 5$ + 1 = 30 + 1 = 31 is prime, so 5 is in the sequence.
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MAPLE
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a := proc(n) select(isprime, select(k -> isprime(A056040(k)+1), [$0..n])) end:
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MATHEMATICA
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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 *)
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PROG
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(PARI) is(k) = isprime(k) && ispseudoprime(1+k!/(k\2)!^2); \\ Jinyuan Wang, Mar 22 2020
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CROSSREFS
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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
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KEYWORD
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nonn,more
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AUTHOR
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Peter Luschny, Jul 21 2009
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EXTENSIONS
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a(8)-a(12) from Robert G. Wilson v, Aug 08 2010
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STATUS
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approved
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