A248031 Least number k such that k^n +- k +- 1 is prime for all four possibilities, or 0 if no such k exists.

3, 15, 6, 0, 30594, 246819, 0, 4033590, 2298429, 0, 19209840, 13542816, 0, 3979836, 75524874, 0, 143635866, 220808901, 0, 14557221, 185958081, 0, 180438825, 320588085, 0, 499478574, 29105421, 0, 37340766, 1169275746, 0, 2051928486, 27069021, 0, 971311320

Offset: 2

Author

Derek Orr, Oct 03 2014

Keywords

• nonn

Comments

a(19) > 155*10^6.

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.

Crossrefs

Cf. A236056, A236764, A236766.

Programs

PARI

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

Extensions

a(19)-a(27) from Jon E. Schoenfield, Oct 19 2014

a(28)-a(36) from Jon E. Schoenfield, Oct 22 2014