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A236173 Primes p such that p^2 - p - 1, p^3 - p - 1 and p^4 - p - 1 are all prime. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A103998 A160587 A034196 * A092044 A156149 A258402

Adjacent sequences:  A236170 A236171 A236172 * A236174 A236175 A236176

KEYWORD

nonn

AUTHOR

Derek Orr, Jan 19 2014

STATUS

approved

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Last modified November 21 22:40 EST 2019. Contains 329383 sequences. (Running on oeis4.)