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

%I A015919 #52 Jun 03 2022 11:06:38
%S A015919 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 A015919 89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,
%U A015919 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 A015919 Positive integers k such that 2^k == 2 (mod k).
%C A015919 Includes 341 which is first pseudoprime to base 2 and distinguishes sequence from A008578.
%C A015919 First composite even term is a(14868) = 161038 = A006935(2). - _Max Alekseyev_, Feb 11 2015
%C A015919 If k is a term, then so is 2^k - 1. - _Max Alekseyev_, Sep 22 2016
%C A015919 Terms of the form 2^k - 2 correspond to k in A296104. - _Max Alekseyev_, Dec 04 2017
%C A015919 If 2^k - 1 is a term, then so is k. - _Thomas Ordowski_, Apr 27 2018
%H A015919 Alois P. Heinz, <a href="/A015919/b015919.txt">Table of n, a(n) for n = 1..20000</a>
%F A015919 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 A015919 Prepend[ Select[ Range@370, PowerMod[2, #, #] == 2 &], {1, 2}] // Flatten (* _Robert G. Wilson v_, May 16 2018 *)
%o A015919 (PARI) is(n)=Mod(2,n)^n==2 \\ _Charles R Greathouse IV_, Mar 11 2014
%o A015919 (Python)
%o A015919 def ok(n): return pow(2, n, n) == 2%n
%o A015919 print([k for k in range(1, 400) if ok(k)]) # _Michael S. Branicky_, Jun 03 2022
%Y A015919 Contains A002997 as a subsequence.
%Y A015919 The odd terms form A176997.
%Y A015919 Cf. A000040, A001567, A008578.
%K A015919 nonn
%O A015919 1,2
%A A015919 _Robert G. Wilson v_