A239503 Numbers n such that n^8+8 and n^8-8 are prime.

3, 1515, 1689, 3327, 4461, 4641, 4965, 5043, 5583, 5709, 6183, 7089, 9291, 9369, 9699, 10125, 11109, 14175, 15081, 18393, 20295, 26955, 27009, 27219, 29067, 30513, 30807, 35355, 35889, 36003, 37935, 40107, 43461, 48045, 49005, 51783, 53289, 55527, 58833, 61203

Offset

1,1

Comments

All numbers are congruent to 3 mod 6.

Intersection of A239345 and A239416.

Links

Table of n, a(n) for n=1..40.

Example

3^8+8 = 6569 is prime and 3^8-8 = 6553 is prime. Thus, 3 is a member of this sequence.

Mathematica

Select[Range[3, 62000, 6], AllTrue[#^8+{8, -8}, PrimeQ]&](* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 07 2020 *)

Prog

(Python)
import sympy
from sympy import isprime
def TwoBoth(x):
..for k in range(10**6):
....if isprime(k**x+x) and isprime(k**x-x):
......print(k)
TwoBoth(8)

Crossrefs

Cf. A239345, A239416.

Sequence in context: A219783 A264427 A285656 * A118050 A246637 A302132

Adjacent sequences: A239500 A239501 A239502 * A239504 A239505 A239506

Keyword

nonn

Author

Derek Orr, Mar 20 2014

Status

approved