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Primes of the form k^k + k + 1.
4

%I #19 Oct 09 2022 11:06:55

%S 2,3,7,31,46663,387420499

%N Primes of the form k^k + k + 1.

%C The associated k are in A058911. - _R. J. Mathar_, Jun 12 2009

%C a(7) = 116035988662615798148247830...0301775295923724561430603629007 (1232 digits).

%F Intersection of A000040 and A066279. - _R. J. Mathar_, Jun 12 2009

%t Unprotect[Power]; Power[0, 0] = 1; Protect[Power]; lst={}; Do[p=n^n+n+1; If[PrimeQ[p], AppendTo[lst,p]], {n,0,100}]; lst

%t Join[{2},Select[Table[k^k+k+1,{k,1000}],PrimeQ]] (* _Harvey P. Dale_, Oct 09 2022 *)

%o (PARI) lista(nn) = for(k=0, nn, if(ispseudoprime(q=k^k+k+1), print1(q, ", "))); \\ _Jinyuan Wang_, Mar 01 2020

%Y Cf. A058911, A066279, A187605.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jun 10 2009

%E Definition simplified by _R. J. Mathar_, Jun 12 2009