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

0,3

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

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 *)

Crossrefs

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

Sequence in context: A276449 A056945 A324472 * A195785 A184187 A106145

Adjacent sequences: A070680 A070681 A070682 * A070684 A070685 A070686

Keyword

nonn,look

Author

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

Status

approved