A070683 Smallest m in range 1..phi(2n+1) such that 12^m == 1 mod 2n+1, or 0 if no such number exists.

0, 0, 4, 6, 0, 1, 2, 0, 16, 6, 0, 11, 20, 0, 4, 30, 0, 12, 9, 0, 40, 42, 0, 23, 42, 0, 52, 4, 0, 29, 15, 0, 4, 66, 0, 35, 36, 0, 6, 26, 0, 41, 16, 0, 8, 6, 0, 12, 16, 0, 100, 102, 0, 53, 54, 0, 112, 44, 0, 48, 11, 0, 100, 126, 0, 65, 6, 0, 136, 138, 0, 2, 4, 0, 148

Offset: 0

Author

N. J. A. Sloane and Amarnath Murthy, May 08 2002

Keywords

• nonn
• look

Comments

a(n)=2*n if 2*n+1 is in A019340, otherwise a(n)<2*n. - Robert Israel, Apr 17 2019

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A070667-A070675, A002326, A019340, A070676, A053447, A070677, A070678, A053451, A070679, A070682, A070680, A070681.

Programs

Maple

f:= proc(n)
  if n mod 3 = 1 then 0 else numtheory:-order(12,2*n+1) fi
end proc:
0, seq(f(n),n=1..100); # Robert Israel, Apr 16 2019

Mathematica

a[n_] := Module[{s}, s = SelectFirst[Range[EulerPhi[2n+1]], PowerMod[12, #, 2n+1] == 1&]; If[s === Missing["NotFound"], 0, s]];
a /@ Range[0, 100] (* Jean-François Alcover, Jun 04 2020 *)