A236171 Numbers k such that k^2 - k - 1, k^3 - k - 1, and k^4 - k - 1 are all prime.

4, 9, 11, 16, 55, 60, 71, 189, 361, 450, 469, 669, 1261, 1351, 1490, 1591, 2101, 2254, 2396, 2594, 3774, 3866, 4011, 5375, 5551, 5840, 6070, 7336, 7545, 7666, 7735, 8105, 8255, 9825, 10525, 11621, 12100, 13084, 13454

Offset: 1

Author

Derek Orr, Jan 19 2014

Keywords

• nonn

Examples

			3866^2 - 3866 - 1, 3866^3 - 3866 - 1, and 3866^4 - 3866 - 1 are all prime, so 3866 is a member of this sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002328, A126421, A126424.

Programs

Mathematica

Select[Range[15000], And @@ PrimeQ[#^Range[2, 4] - # - 1] &] (* Amiram Eldar, Mar 21 2020 *)

PARI

s=[]; for(n=1, 20000, if(isprime(n^2-n-1) && isprime(n^3-n-1) && isprime(n^4-n-1), s=concat(s, n))); s \\ Colin Barker, Jan 20 2014

Python

import sympy
from sympy import isprime
{print(n) for n in range(10**5) if isprime(n**2-n-1) and isprime(n**3-n-1) and isprime(n**4-n-1)}