A015919 - OEIS

%I #52 Jun 03 2022 11:06:38

%S 1,2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,

%T 89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,

%U 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

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

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

%C First composite even term is a(14868) = 161038 = A006935(2). - _Max Alekseyev_, Feb 11 2015

%C If k is a term, then so is 2^k - 1. - _Max Alekseyev_, Sep 22 2016

%C Terms of the form 2^k - 2 correspond to k in A296104. - _Max Alekseyev_, Dec 04 2017

%C If 2^k - 1 is a term, then so is k. - _Thomas Ordowski_, Apr 27 2018

%H Alois P. Heinz, <a href="/A015919/b015919.txt">Table of n, a(n) for n = 1..20000</a>

%F 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

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

%o (PARI) is(n)=Mod(2,n)^n==2 \\ _Charles R Greathouse IV_, Mar 11 2014

%o (Python)

%o def ok(n): return pow(2, n, n) == 2%n

%o print([k for k in range(1, 400) if ok(k)]) # _Michael S. Branicky_, Jun 03 2022

%Y Contains A002997 as a subsequence.

%Y The odd terms form A176997.

%Y Cf. A000040, A001567, A008578.

%K nonn

%O 1,2

%A _Robert G. Wilson v_