A057195 Numbers k such that 2^k + 7 is prime.

2, 4, 6, 8, 10, 16, 18, 20, 28, 30, 38, 44, 78, 88, 98, 126, 160, 174, 204, 214, 588, 610, 798, 926, 1190, 1198, 1806, 1888, 2648, 3454, 3510, 3864, 3870, 8970, 12330, 13330, 18876, 22338, 39718, 55006, 110784, 172470, 196434, 235710, 247280, 268408, 279320, 300874, 315268, 372950, 472258, 566496, 780284, 820356

Offset: 1

Author

Robert G. Wilson v, Sep 15 2000

Keywords

• nonn

Comments

Naturally all terms are even because (3-1)^(2n+1)+7 is divisible by 3. - Bruno Berselli, Oct 03 2012

Links

• Keith Conrad, Square patterns and infinitude of primes, University of Connecticut, 2019.
• Jon Grantham and Andrew Granville, Fibonacci primes, primes of the form 2^n-k and beyond, arXiv:2307.07894 [math.NT], 2023.

Crossrefs

Cf. A104066 (primes of the form 2^k+7).

Programs

Maple

A057195:=n->if isprime(2^n+7) then n; fi; seq(A057195(n), n=1..1000); # Wesley Ivan Hurt, Dec 06 2013

Mathematica

Do[ If[ PrimeQ[ 2^n +7 ], Print[n]], { n, 1, 15000 }]

PARI

is(n)=isprime(2^n+7) \\ Charles R Greathouse IV, Feb 17 2017

Formula

a(n) = 2*A217349(n). - Elmo R. Oliveira, Nov 12 2023

Extensions

a(37)-a(51) from Robert Price, Dec 06 2013

a(51), a(53), a(54) from Jon Grantham, Jul 29 2023