A103498 Multiplicative suborder of 12 (mod 2n+1) = sord(12, 2n+1).

0, 0, 2, 3, 0, 1, 1, 0, 8, 3, 0, 11, 10, 0, 2, 15, 0, 12, 9, 0, 20, 21, 0, 23, 21, 0, 26, 4, 0, 29, 15, 0, 4, 33, 0, 35, 18, 0, 6, 13, 0, 41, 16, 0, 4, 3, 0, 12, 8, 0, 50, 51, 0, 53, 27, 0, 56, 44, 0, 48, 11, 0, 50, 63, 0, 65, 3, 0, 68, 69, 0, 2, 2, 0, 74, 75, 0, 60, 3, 0, 66, 81, 0, 83, 13, 0

Offset

0,3

Comments

a(n) is minimum e for which 12^e = +/-1 mod 2n+1, or zero if no e exists.

References

H. Cohen, Course in Computational Algebraic Number Theory, Springer, 1993, p. 25, Algorithm 1.4.3

Links

Table of n, a(n) for n=0..85.

Eric Weisstein's World of Mathematics, Multiplicative Order

S. Wolfram, Algebraic Properties of Cellular Automata (1984), Appendix B.

Mathematica

Suborder[k_, n_] := If[n > 1 && GCD[k, n] == 1, Min[MultiplicativeOrder[k, n, {-1, 1}]], 0];
a[n_] := Suborder[12, 2 n + 1];
a /@ Range[0, 100] (* Jean-François Alcover, Mar 21 2020, after T. D. Noe in A003558 *)

Crossrefs

Sequence in context: A135814 A038570 A306559 * A030386 A096799 A370292

Adjacent sequences: A103495 A103496 A103497 * A103499 A103500 A103501

Keyword

easy,nonn

Author

Harry J. Smith, Feb 11 2005

Status

approved