A248031 - OEIS

%I #45 Jan 16 2021 01:29:16

%S 3,15,6,0,30594,246819,0,4033590,2298429,0,19209840,13542816,0,

%T 3979836,75524874,0,143635866,220808901,0,14557221,185958081,0,

%U 180438825,320588085,0,499478574,29105421,0,37340766,1169275746,0,2051928486,27069021,0,971311320

%N Least number k such that k^n +- k +- 1 is prime for all four possibilities, or 0 if no such k exists.

%C a(19) > 155*10^6.

%C For n == 2 (mod 3), k^n + k + 1 is divisible by k^2 + k + 1. Thus, for n > 2, if n == 2 (mod 3), a(n) = 0.

%o (PARI)

%o a(n)=if(n>2&&n==Mod(2,3),return(0));k=1;while(!ispseudoprime(k^n+k+1)||!ispseudoprime(k^n+k-1)||!ispseudoprime(k^n-k+1)||!ispseudoprime(k^n-k-1),k++);k

%o n=2;while(n<100,print1(a(n),", ");n++)

%Y Cf. A236056, A236764, A236766.

%K nonn

%O 2,1

%A _Derek Orr_, Oct 03 2014

%E a(19)-a(27) from _Jon E. Schoenfield_, Oct 19 2014

%E a(28)-a(36) from _Jon E. Schoenfield_, Oct 22 2014