A236173 Primes p such that p^2 - p - 1, p^3 - p - 1 and p^4 - p - 1 are all prime.

11, 71, 11621, 28151, 32089, 37501, 39209, 45329, 66161, 76649, 114599, 122131, 136949, 154991, 202999, 228901, 243391, 270269, 296911, 313909, 318679, 333701, 343309, 359291, 369979, 371281, 371981, 373171, 373459

Offset

1,1

Comments

Primes in A236171. All primes appear to end in a 1 or a 9 (congruent to either 1 mod 10 or 9 mod 10).

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

228901 is prime, 228901^2 - 228901 - 1 is prime, 228901^3 - 228901 - 1 is prime, and 228901^4 - 228901 - 1 is prime. So 228901 is a member of this sequence.

Mathematica

Select[Prime[Range[32000]], AllTrue[#^{2, 3, 4}-#-1, PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 08 2019 *)

Prog

(Python)
import sympy
from sympy import isprime
{print(p) for p in range(10**6) if isprime(p) and isprime(p**2-p-1) and isprime(p**3-p-1) and isprime(p**4-p-1)}
(PARI)
s=[]; forprime(p=2, 400000, if(isprime(p^2-p-1) && isprime(p^3-p-1) && isprime(p^4-p-1), s=concat(s, p))); s \\ Colin Barker, Jan 20 2014

Crossrefs

Cf. A091567, A236168, A236071.

Sequence in context: A160587 A338416 A034196 * A092044 A156149 A258402

Adjacent sequences: A236170 A236171 A236172 * A236174 A236175 A236176

Keyword

nonn

Author

Derek Orr, Jan 19 2014

Status

approved