A236764 Numbers k such that k^3 +/- k +/- 1 are prime for all four possibilities.

15, 21, 15375, 25164, 53361, 95190, 110685, 115140, 133701, 139425, 140430, 140844, 189336, 217686, 220650, 266916, 272469, 289341, 344880, 364665, 377805, 382221, 390270, 415779, 454905, 539700, 561186, 567645, 575799, 584430, 603651, 722484

Offset: 1

Author

Derek Orr, Jan 30 2014

Keywords

• nonn

Examples

			110685^3+110685+1 (1356020665779811), 110685^3+110685-1 (1356020665779809), 110685^3-110685+1 (1356020665558441) and 110685^3-110685-1 (1356020665558439) are all prime. Thus 110685 is a member of this sequence.
		

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A126421, A236477, A049407, and A236475.

Programs

PARI

for(n=1, 800000, if(isprime(n^3+n+1)&&isprime(n^3-n+1)&&isprime(n^3+n-1)&&isprime(n^3-n-1), print1(n, ","))) \\ Colin Barker, Jan 31 2014

Python

import sympy
from sympy import isprime
{print(n) for n in range(10**6) if isprime(n**3+n+1) and isprime(n**3-n+1) and isprime(n**3+n-1) and isprime(n**3-n-1)}