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%I #18 Dec 15 2023 13:53:25
%S 1,3,737,1349
%N Numbers k such that k^k+2 is prime.
%C All terms are odd. Next term is greater than 3500. 1349^1349+2 is a probable prime with length 4223.
%C The next term, if it exists, is greater than 50000. - _Hugo Pfoertner_, Jun 28 2019
%C The next term, if it exists, is greater than 430000. - _Ryan Propper_, Dec 15 2023
%e 737 is in the sequence because 737^737+2 is prime.
%t Do[If[PrimeQ[n^n+2], Print[n]], {n, 3500}]
%o (PARI) is(n)=ispseudoprime(n^n+2) \\ _Charles R Greathouse IV_, May 22 2017
%Y Cf. A100408.
%K more,nonn,hard
%O 1,2
%A _Farideh Firoozbakht_, Nov 19 2004