A268607 a(n) is the least m > 1 such that 2^n - m is prime.

2, 3, 3, 3, 3, 15, 5, 3, 3, 9, 3, 13, 3, 19, 15, 9, 5, 19, 3, 9, 3, 15, 3, 39, 5, 39, 57, 3, 35, 19, 5, 9, 41, 31, 5, 25, 45, 7, 87, 21, 11, 57, 17, 55, 21, 115, 59, 81, 27, 129, 47, 111, 33, 55, 5, 13, 27, 55, 93, 31, 57, 25, 59, 49, 5, 19, 23, 19, 35, 231, 93

Offset: 2

Author

Alexei Kourbatov, Feb 08 2016

Keywords

• nonn

Comments

a(1) is not defined (there are no primes less than 2).

The definition is similar to Lesser Fortunate numbers (A055211) but uses 2^n instead of primorials A002110(n).

Examples

			a(7)=15 because m=15 is the least m > 1 such that 2^7 - m is prime.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A005235, A013603, A055211, A264050, A263925, A268608.

Programs

Mathematica

Map[# - NextPrime[#-1, -1] &, 2^Range[2, 100]] (* Paolo Xausa, Mar 10 2025 *)

PARI

a(n)=2^n-precprime(2^n-2)

Formula

a(n) = A013603(n), if A013603(n) > 1. - Jason Yuen, Mar 10 2025