A059608 Numbers k such that 2^k - 5 is prime.

3, 4, 6, 8, 10, 12, 18, 20, 26, 32, 36, 56, 66, 118, 130, 150, 166, 206, 226, 550, 706, 810, 1136, 1228, 1818, 2368, 2400, 3128, 4532, 5112, 8492, 16028, 16386, 17392, 18582, 21986, 24292, 27618, 30918, 32762, 48212, 120440, 183632, 316140, 364982, 414032, 533350, 595122

Offset: 1

Author

Andrey V. Kulsha, Jan 30 2001

Keywords

• nonn

Comments

Except 3, all terms are even since for odd k, 2^k - 5 is divisible by 3.

Examples

			k = 10: 2^10 - 5 = 1019 is prime.
k = 20: 2^20 - 5 = 1048571 is prime.
		

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.
• Henri Lifchitz and Renaud Lifchitz (Editors), Search for 2^n-5, PRP Top Records.

Crossrefs

Cf. Sequences of numbers k such that 2^k - d is prime: A000043 (d=1), A050414 (d=3), this sequence (d=5), A059609 (d=7), A059610 (d=9), A096817 (d=11), A096818 (d=13), A059612 (d=15), A059611 (d=17), A096819 (d=19), A096820 (d=21), A057220 (d=23), A356826 (d=29).

Programs

Mathematica

Select[Range[2, 20000],PrimeQ[2^# - 5] &] (* Vladimir Joseph Stephan Orlovsky, Feb 26 2011 *)

PARI

is(n)=isprime(2^n-5) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(32)-a(34) from Labos Elemer, Jul 09 2004

a(35)-a(40) from Max Alekseyev, a(41) from Paul Underwood, a(42)-a(46) from Henri Lifchitz, added by Max Alekseyev, Feb 09 2012

a(47)-a(48) from Jon Grantham, Jul 29 2023