A019340 -id:A019340 - cp's OEIS frontend

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

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

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

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

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

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

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 *)

A061325 Primes with 12 as smallest positive primitive root.

Original entry on oeis.org

4111, 7841, 10111, 15391, 15991, 16061, 20011, 21031, 22699, 32299, 32957, 35911, 43963, 45127, 45631, 47431, 49831, 51199, 53731, 58111, 59671, 60331, 64231, 74311, 76039, 78079, 81331, 81761, 83311, 83431, 98911, 102871, 104729, 108907

Offset: 1

Klaus Brockhaus, Apr 24 2001

nonn

T. D. Noe, Table of n, a(n) for n=1..1000

Cf. A001918, A001126, A019340.

Prime[ Select[ Range[15000], PrimitiveRoot[ Prime[ # ] ] == 12 & ] ]
(* or *)
Select[ Prime@Range@15000, PrimitiveRoot@# == 12 &] (* Robert G. Wilson v, May 11 2001 *)

cp's OEIS Frontend

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

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