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%I #17 Nov 03 2021 21:28:47
%S 0,2,4,12,18,36
%N Numbers n such that n!*2^n + n + 1 = A000165(n) + n + 1 is prime.
%C For comparison, A000165(n)+1 is prime for n = 0, 1, 259, 16708, 18655,... (A256594).
%C a(6) > 25000, if it exists. - _Giovanni Resta_, Jun 01 2018
%e n=4, 2^4*4! + 4 + 1 = 389 is prime.
%t Select[Range[100], PrimeQ[#! 2^# + # + 1] &] (* _Giovanni Resta_, May 31 2018 *)
%Y Cf. A000165, A052290, A256594.
%K nonn,more
%O 1,2
%A _Labos Elemer_, Feb 08 2000
%E a(1)=0 inserted by _Sean A. Irvine_, Nov 03 2021