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%I #10 May 08 2020 17:43:45
%S 3,5,7,13,41,47,83,137,151,229,317,389,1063,2371,6101,7873,13007,19603
%N Primes p such that p$ - 1 is also prime. Here '$' denotes the swinging factorial function (A056040).
%C a(n) are the primes in A163078.
%H Peter Luschny, <a href="/A180000/a180000.pdf">Die schwingende Fakultät und Orbitalsysteme</a>, August 2011.
%H Peter Luschny, <a href="http://www.luschny.de/math/primes/SwingingPrimes.html"> Swinging Primes.</a>
%e 3 is prime and 3$ - 1 = 5 is prime, so 3 is in the sequence.
%p a := proc(n) select(isprime,select(k -> isprime(A056040(k)-1),[$0..n])) end:
%t sf[n_] := n!/Quotient[n, 2]!^2; Select[Prime /@ Range[200], PrimeQ[sf[#] - 1] &] (* _Jean-François Alcover_, Jun 28 2013 *)
%o (PARI) is(k) = isprime(k) && ispseudoprime(k!/(k\2)!^2-1); \\ _Jinyuan Wang_, Mar 22 2020
%Y Cf. A056040, A103317, A163079, A163078.
%K nonn,more
%O 1,1
%A _Peter Luschny_, Jul 21 2009
%E a(14)-a(18) from _Jinyuan Wang_, Mar 22 2020
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