A103495 Multiplicative suborder of 9 (mod n) = sord(9, n).

0, 0, 1, 0, 1, 1, 0, 3, 1, 0, 1, 5, 0, 3, 3, 0, 2, 4, 0, 9, 2, 0, 5, 11, 0, 5, 3, 0, 3, 7, 0, 15, 4, 0, 4, 6, 0, 9, 9, 0, 2, 2, 0, 21, 5, 0, 11, 23, 0, 21, 5, 0, 3, 13, 0, 10, 3, 0, 7, 29, 0, 5, 15, 0, 8, 6, 0, 11, 8, 0, 6, 35, 0, 3, 9, 0, 9, 15, 0, 39, 2, 0, 2, 41, 0, 8, 21, 0, 5, 22, 0, 3, 11, 0, 23

Offset

0,8

Comments

a(n) is minimum e for which 9^e = +/-1 mod n, 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..94.

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[9, n];
a /@ Range[0, 100] (* Jean-François Alcover, Mar 21 2020, after T. D. Noe in A003558 *)

Crossrefs

Sequence in context: A085391 A280880 A050143 * A261699 A285574 A354821

Adjacent sequences: A103492 A103493 A103494 * A103496 A103497 A103498

Keyword

easy,nonn

Author

Harry J. Smith, Feb 08 2005

Status

approved