

A070683


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


11



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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] (* JeanFrançois Alcover, Jun 04 2020 *)


CROSSREFS

Cf. A070667A070675, 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



