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

1,2

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

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

Mathematica

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

Prog

(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

Crossrefs

Contains A002997 as a subsequence.

The odd terms form A176997.

Cf. A000040, A001567, A008578.

Sequence in context: A216886 A273960 A100726 * A352190 A324050 A064555

Adjacent sequences: A015916 A015917 A015918 * A015920 A015921 A015922

Keyword

nonn

Author

Robert G. Wilson v

Status

approved