A015919 Positive integers k such that 2^k == 2 (mod k).

1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 341, 347, 349, 353, 359, 367

Offset: 1

Author

Robert G. Wilson v

Keywords

• nonn

Comments

Includes 341 which is first pseudoprime to base 2 and distinguishes sequence from A008578.

First composite even term is a(14868) = 161038 = A006935(2). - Max Alekseyev, Feb 11 2015

If k is a term, then so is 2^k - 1. - Max Alekseyev, Sep 22 2016

Terms of the form 2^k - 2 correspond to k in A296104. - Max Alekseyev, Dec 04 2017

If 2^k - 1 is a term, then so is k. - Thomas Ordowski, Apr 27 2018

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

Contains A002997 as a subsequence.

The odd terms form A176997.

Cf. A000040, A001567, A008578.

Programs

Mathematica

Prepend[ Select[ Range@370, PowerMod[2, #, #] == 2 &], {1, 2}] // Flatten (* Robert G. Wilson v, May 16 2018 *)

PARI

is(n)=Mod(2,n)^n==2 \\ Charles R Greathouse IV, Mar 11 2014

Python

def ok(n): return pow(2, n, n) == 2%n
print([k for k in range(1, 400) if ok(k)]) # Michael S. Branicky, Jun 03 2022

Formula

Equals {1} U A000040 U A001567 U A006935 = A001567 U A006935 U A008578. - Ray Chandler, Dec 07 2003; corrected by Max Alekseyev, Feb 11 2015