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A163077 Numbers k such that k$ + 1 is prime. Here '$' denotes the swinging factorial function (A056040).

%I A163077 #11 May 08 2020 17:46:42
%S A163077 0,1,2,3,4,5,8,9,14,15,24,27,31,38,44,45,49,67,76,92,99,119,124,133,
%T A163077 136,139,144,168,171,185,265,291,332,368,428,501,631,680,689,696,765,
%U A163077 789,890,1034,1233,1384,1517,1615,1634,1809,2632,2762,3925,4419,5108,5426
%N A163077 Numbers k such that k$ + 1 is prime. Here '$' denotes the swinging factorial function (A056040).
%H A163077 Peter Luschny, <a href="/A180000/a180000.pdf">Die schwingende Fakultät und Orbitalsysteme</a>, August 2011.
%H A163077 Peter Luschny, <a href="http://www.luschny.de/math/primes/SwingingPrimes.html"> Swinging Primes.</a>
%e A163077 0$ + 1 = 1 + 1 = 2 is prime, so 0 is in the sequence.
%p A163077 a := proc(n) select(x -> isprime(A056040(x)+1),[$0..n]) end:
%t A163077 fQ[n_] := PrimeQ[1 + 2^(n - Mod[n, 2])*Product[k^((-1)^(k + 1)), {k, n}]]; Select[ Range[0, 8660], fQ] (* _Robert G. Wilson v_, Aug 09 2010 *)
%o A163077 (PARI) is(k) = ispseudoprime(1+k!/(k\2)!^2); \\ _Jinyuan Wang_, Mar 22 2020
%Y A163077 Cf. A002981, A163078, A163079, A163080.
%K A163077 nonn
%O A163077 1,3
%A A163077 _Peter Luschny_, Jul 21 2009
%E A163077 a(45)-a(56) from _Robert G. Wilson v_, Aug 09 2010