A243400 Primes p such that p^6 - p^5 - p^4 - p^3 - p^2 - p - 1 is prime.

5, 7, 17, 37, 79, 157, 239, 269, 277, 359, 419, 449, 467, 557, 677, 739, 787, 829, 857, 977, 1319, 1399, 1597, 1657, 2069, 2269, 2297, 2377, 2437, 2459, 2819, 2969, 2999, 3019, 3137, 3299, 3389, 3407, 3967, 4007, 4099, 4357, 4547, 4729, 4987, 5179, 5419, 5569, 5779, 6637

Offset

1,1

Comments

a(1) = 5 is the only term that ends in a 5. It is unknown if any term will end in a 3 or 1.

In the first 100,000 primes, no term ends in a 3 or 1. - Harvey P. Dale, Oct 13 2023

Links

Table of n, a(n) for n=1..50.

Example

5 is prime and 5^6 - 5^5 - 5^4 - 5^3 - 5^2 - 5 - 1 = 11719 is prime. Thus 5 is a member of this sequence.

Mathematica

Select[Prime[Range[1000]], PrimeQ[#^6-Total[#^Range[0, 5]]]&] (* Harvey P. Dale, Oct 13 2023 *)

Prog

(Python)
import sympy
from sympy import isprime
{print(n, end=', ') for n in range(10**4) if isprime(n**6-n**5-n**4-n**3-n**2-n-1) and isprime(n)}
(PARI) for(n=1, 10^4, if(ispseudoprime(n)&&ispseudoprime(n^6-sum(i=0, 5, n^i)), print1(n, ", ")))

Crossrefs

Cf. A243300.

Sequence in context: A272717 A018538 A038968 * A318568 A239414 A163570

Adjacent sequences: A243397 A243398 A243399 * A243401 A243402 A243403

Keyword

nonn

Author

Derek Orr, Jun 04 2014

Status

approved