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

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, 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, 20, 50, 1, 7, 2, 3, 36, 1, 2, 23, 60, 7, 42, 2, 1, 6, 20, 2

Offset: 0

Author

Vincenzo Librandi, Jan 03 2016

Keywords

• nonn
• easy

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Multiplicative Order

Crossrefs

Cf. A002326, A053447, A053451.

Programs

GAP

List([0..100],n->OrderMod(2^n,2*n+1)); # Muniru A Asiru, Feb 25 2019

Magma

[1] cat [Modorder(2^n, 2*n+1): n in [1..100]];

Maple

1,seq(numtheory:-order(2^n,2*n+1),n=1..100); # Robert Israel, Jan 10 2016

Mathematica

Table[MultiplicativeOrder[2^n, 2 n + 1], {n, 0, 100}]

PARI

a(n) = if(n<0, 0, znorder(Mod(2^n, 2*n+1))); \\ Altug Alkan, Jan 04 2016

Formula

a(n) = A002326(n)/gcd(n,A002326(n)). - Robert Israel, Jan 10 2016