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

1,1

Links

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

Example

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

Mathematica

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

Prog

(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)}
(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

Crossrefs

Cf. A002328, A126421, A126424.

Sequence in context: A336826 A212017 A362505 * A312838 A312839 A312840

Adjacent sequences: A236168 A236169 A236170 * A236172 A236173 A236174

Keyword

nonn

Author

Derek Orr, Jan 19 2014

Status

approved