A239503 - OEIS

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

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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