A216829 -id:A216829 - cp's OEIS frontend

A216833 Multiplicative order of 2 mod 3*(2n-1).

2, 6, 4, 6, 18, 10, 12, 12, 8, 18, 6, 22, 20, 54, 28, 10, 30, 12, 36, 12, 20, 14, 36, 46, 42, 24, 52, 20, 18, 58, 60, 18, 12, 66, 66, 70, 18, 60, 30, 78, 162, 82, 8, 84, 22, 12, 30, 36, 48, 90, 100, 102, 12, 106, 36, 36, 28, 44, 36, 24, 110, 60, 100, 14, 42

Offset: 1

V. Raman, Sep 17 2012

nonn

a(n) is the smallest m such that 3*(2n-1) | (2^m+1).

Muniru A Asiru, Table of n, a(n) for n = 1..10000

Cf. A003558, A002326, A216469, A216829.

List([1..70],n->OrderMod(2,3*(2*n-1))); # Muniru A Asiru, Feb 25 2019

Table[MultiplicativeOrder[2, 3*(2*n-1)], {n, 100}] (* T. D. Noe, Sep 19 2012 *)

vector(100,n,znorder(Mod(2,3*(2*n-1)))) \\ Joerg Arndt, Sep 14 2012.

a(n) = 2*A216829(n).

A216469 a(n) = smallest m such that 2n-1 | (2^m+1)/3, or 0 if no such m exists.

Original entry on oeis.org

1, 3, 0, 0, 9, 5, 0, 0, 0, 9, 0, 0, 0, 27, 0, 0, 15, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 9, 29, 0, 0, 0, 33, 0, 0, 0, 0, 0, 0, 81, 41, 0, 0, 0, 0, 0, 0, 0, 45, 0, 0, 0, 53, 0, 0, 0, 0, 0, 0, 55, 0, 0, 0, 21, 65, 0, 0, 0, 69, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 81, 0, 0

Offset: 1

V. Raman, Sep 07 2012

nonn

Cf. A003558, A002326, A216829, A216833.
Cf. A216833 (multiplicative order of 2 mod 3*(2n-1)).
Cf. A216829 (value of the half of the multiplicative order of 2 mod 3*(2n-1)).

Table[s = MultiplicativeOrder[2, 3*(2*n-1), {-1}]; If[IntegerQ[s], s, 0], {n, 100}] (* T. D. Noe, Sep 11 2012 *)

for(i=0,200,i++;m=0;for(x=0,i,x++;if(((2^x+1)/3)%i==0,m=x;break));print1(m",")) \\ V. Raman, Nov 22 2012

cp's OEIS Frontend

A216833 Multiplicative order of 2 mod 3*(2n-1).

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