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

1,2

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

Links

Table of n, a(n) for n=1..29.

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A245510.

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

Sequence in context: A317702 A214001 A252136 * A332190 A015278 A352441

Adjacent sequences: A216927 A216928 A216929 * A216931 A216932 A216933

Keyword

nonn

Author

Michel Lagneau, Sep 20 2012

Status

approved