A160215 Primes congruent to 2^k+1 (mod 2^(k+1)), where k is any even integer >=0.

2, 5, 13, 17, 29, 37, 53, 61, 101, 109, 113, 149, 157, 173, 181, 193, 197, 229, 241, 257, 269, 277, 293, 317, 337, 349, 373, 389, 397, 401, 421, 433, 449, 461, 509, 541, 557, 577, 593, 613, 653, 661, 677, 701, 709, 733, 757, 769, 773, 797, 821, 829, 853, 877

Offset: 1

Author

Vladimir Shevelev, May 04 2009

Keywords

• nonn

Comments

If A(x) is the counting function of the terms not exceeding x, then A(x) grows similarly to Pi(x)/3, see A000720.

Lim_{x -> inf.} the number of terms < x in A160216/A160215 => 2. - Robert G. Wilson v, May 31 2009

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A000040.

Programs

Mathematica

fQ[n_] := Mod[ Flatten[ FactorInteger[n - 1]] [[2]], 2] == 0; Select[ Prime@ Range@ 155, fQ@# &] (* Robert G. Wilson v, May 31 2009 *)

Formula

A000040 \ A160216.

{prime(k) : A023506(k) is even}. - R. J. Mathar, May 08 2009

Extensions

Edited by R. J. Mathar, May 08 2009

More terms from Robert G. Wilson v, May 31 2009