cp's OEIS Frontend

A129492 Composite numbers k such that 2^k mod k is a power of 2.

%I A129492 #11 Aug 20 2023 17:01:32
%S A129492 6,9,10,12,14,15,20,21,22,24,26,28,30,33,34,38,39,40,44,46,48,51,52,
%T A129492 56,57,58,60,62,63,65,66,68,69,72,74,76,78,80,82,84,85,86,87,90,92,93,
%U A129492 94,96,102,106,111,112,114,116,118,120,122,123,124,126,129,132,133,134,138
%N A129492 Composite numbers k such that 2^k mod k is a power of 2.
%C A129492 Complement to composite numbers: 4, 8, 16, 18, 25, 27, 32, 35, 36, 42, 45, 49, 50, 54, 55, 64, 70, 75, 77, 81, 88, 91, 95, 98, 99, ....
%H A129492 Robert Israel, <a href="/A129492/b129492.txt">Table of n, a(n) for n = 1..10000</a>
%e A129492 15 is a term since 2^15 mod 15 = 8.
%p A129492 filter:= proc(n) local k;
%p A129492   if isprime(n) then return false fi;
%p A129492   k:= 2 &^ n mod n;
%p A129492   k > 1 and k = 2^padic:-ordp(k,2)
%p A129492 end proc:
%p A129492 select(filter, [$4..1000]); # _Robert Israel_, Dec 03 2019
%t A129492 Select[Range@ 141, IntegerQ@ Log[2, PowerMod[2, #, # ]] &]
%o A129492 (Magma) [k:k in [2..150]| not IsPrime(k)  and  not IsZero(a)  and (PrimeDivisors(a) eq [2]) where a is 2^k mod k ]; // _Marius A. Burtea_, Dec 04 2019
%Y A129492 Cf. A036236, A129493, A129494, A129495, A129496, A129497.
%Y A129492 Contains A001567.
%K A129492 easy,nonn
%O A129492 1,1
%A A129492 _Robert G. Wilson v_, Apr 17 2007