A104080 Smallest prime >= 2^n.

2, 2, 5, 11, 17, 37, 67, 131, 257, 521, 1031, 2053, 4099, 8209, 16411, 32771, 65537, 131101, 262147, 524309, 1048583, 2097169, 4194319, 8388617, 16777259, 33554467, 67108879, 134217757, 268435459, 536870923, 1073741827, 2147483659

Offset: 0

Author

Cino Hilliard, Mar 03 2005

Keywords

• easy
• nonn

Links

• Jinyuan Wang, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A104081, A338475.

Except initial terms and offset, same as A014210 and A203074.

The opposite (greatest prime <= 2^n) is A014234, indices A007053.

The distance from 2^n is A092131, opposite A013603.

Counting zeros instead of both bits gives A372474, cf. A035103, A211997.

Counting ones instead of both bits gives A372517, cf. A014499, A061712.

For squarefree instead of prime we have A372683, cf. A143658, A372540.

The indices of these prime are given by A372684.

Cf. A007918, A007920, A029837, A035100, A049095, A130739.

Programs

Mathematica

Join[{2,2},NextPrime[#]&/@(2^Range[2,40])]  (* Harvey P. Dale, Jan 26 2011 *)
NextPrime[2^Range[0,50]-1]  (* Vladimir Joseph Stephan Orlovsky, Apr 11 2011 *)

PARI

g(n,b=2) = for(x=0,n,print1(nextprime(b^x)","))

PARI

a(n) = nextprime(2^n); \\ Michel Marcus, Nov 01 2020

Formula

a(n) = A014210(n), n <> 1. - R. J. Mathar, Oct 14 2008

Sum_{n >= 0} 1/a(n) = A338475 + 1/6 = 1.4070738... (because 1/6 = 1/2 - 1/3). - Bernard Schott, Nov 01 2020

From Gus Wiseman, Jun 03 2024: (Start)

a(n) = A007918(2^n).

a(n) = 2^n + A092131(n).

a(n) = prime(A372684(n)).

(End)