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%I #27 Nov 12 2024 14:31:49
%S 1,2,4,28,496
%N Numbers k such that k^k + k! + 1 is prime.
%C These primes are of the form: A000312(n) + A000142(n) + 1.
%C Note that 28 and 496 are perfect numbers (see A000396).
%C a(6) > 1500.
%C a(6) > 25000. - _Michael S. Branicky_, Nov 12 2024
%e For n = 1, 1^1 + 1! + 1 = 3, which is prime.
%e For n = 2, 2^2 + 2! + 1 = 4 + 2 + 1 = 7, which is prime.
%e For n = 4, 4^4 + 4! + 1 = 281, which is prime.
%t Select[Range[1500], PrimeQ[#^# + #! + 1]&]
%o (PARI) for(n=1,10^3,if(ispseudoprime(n^n+n!+1),print1(n,", "))) \\ _Derek Orr_, Mar 06 2015
%Y Cf. A000312 (n^n), A000142(n!).
%K nonn,more,hard
%O 1,2
%A _Waldemar Puszkarz_, Mar 04 2015