cp's OEIS Frontend

A266697 Multiplicative order of 2^n mod 2*n+1.

%I A266697 #16 Feb 16 2025 08:33:28
%S A266697 1,2,2,1,3,2,2,4,1,2,3,1,5,18,2,1,5,12,2,12,1,2,6,1,7,8,2,20,9,2,2,6,
%T A266697 3,2,11,1,1,20,15,1,27,2,4,28,1,4,5,36,1,30,2,1,3,2,2,36,1,44,6,24,11,
%U A266697 20,50,1,7,2,3,36,1,2,23,60,7,42,2,1,6,20,2
%N A266697 Multiplicative order of 2^n mod 2*n+1.
%H A266697 Robert Israel, <a href="/A266697/b266697.txt">Table of n, a(n) for n = 0..10000</a>
%H A266697 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MultiplicativeOrder.html">Multiplicative Order</a>
%F A266697 a(n) = A002326(n)/gcd(n,A002326(n)). - _Robert Israel_, Jan 10 2016
%p A266697 1,seq(numtheory:-order(2^n,2*n+1),n=1..100); # _Robert Israel_, Jan 10 2016
%t A266697 Table[MultiplicativeOrder[2^n, 2 n + 1], {n, 0, 100}]
%o A266697 (Magma) [1] cat [Modorder(2^n, 2*n+1): n in [1..100]];
%o A266697 (PARI) a(n) = if(n<0, 0, znorder(Mod(2^n, 2*n+1))); \\ _Altug Alkan_, Jan 04 2016
%o A266697 (GAP) List([0..100],n->OrderMod(2^n,2*n+1)); # _Muniru A Asiru_, Feb 25 2019
%Y A266697 Cf. A002326, A053447, A053451.
%K A266697 nonn,easy
%O A266697 0,2
%A A266697 _Vincenzo Librandi_, Jan 03 2016