A216930 Numbers k such that k + 2, k^2 + 2, k^3 + 2, k^4 + 2 and k^5 + 2 are all prime.

1, 909, 11925, 358875, 959595, 1047585, 3673089, 3925635, 3973971, 4995825, 5519241, 6516015, 6832245, 7217805, 7422381, 9145809, 10929765, 11038071, 11477235, 11721291, 12015555, 12262791, 12280935, 13454349, 13508475, 14625849, 15320829, 15321489, 15332745

Offset: 1

Author

Michel Lagneau, Sep 20 2012

Keywords

• nonn

Comments

k^6 + 2 is also prime for k = 4995825, 11038071, ...

a(2) = 909 = A245510(6); a(10) = 4996825, the first k such that k^6 + 2 is also prime, is A245510(7). - Jon E. Schoenfield, Dec 24 2022

Crossrefs

Cf. A245510.

Intersection of A040976, A067201, A067200, A216974, and A216976.

Programs

Mathematica

Select[Range[16000000], And@@PrimeQ/@(Table[n^i+2, {i, 1, 5}]/.n->#)&]
Select[Range[16*10^6], AllTrue[2 + #^Range[5], PrimeQ] &] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jun 24 2015 *)

Python

from sympy import isprime
def ok(n): return all(isprime(n**i+2) for i in range(1, 6))
print([k for k in range(1, 2*10**7, 2) if ok(k)]) # Michael S. Branicky, Dec 24 2022

Formula

a(n) == 3 (mod 6) for n>1. - Alexandru Petrescu, Dec 24 2022