A103489 Multiplicative suborder of 3 (mod n) = sord(3, n).

0, 0, 1, 0, 1, 2, 0, 3, 2, 0, 2, 5, 0, 3, 3, 0, 4, 8, 0, 9, 4, 0, 5, 11, 0, 10, 3, 0, 3, 14, 0, 15, 8, 0, 8, 12, 0, 9, 9, 0, 4, 4, 0, 21, 10, 0, 11, 23, 0, 21, 10, 0, 6, 26, 0, 20, 6, 0, 14, 29, 0, 5, 15, 0, 16, 12, 0, 11, 16, 0, 12, 35, 0, 6, 9, 0, 9, 30, 0, 39, 4, 0, 4, 41, 0, 16, 21, 0, 10, 44

Offset

0,6

Comments

a(n) is minimum e for which 3^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..89.

Eric Weisstein's World of Mathematics, Multiplicative Order.

Eric Weisstein's World of Mathematics, Suborder Function

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

Crossrefs

Sequence in context: A257541 A120854 A035159 * A213944 A127479 A284124

Adjacent sequences: A103486 A103487 A103488 * A103490 A103491 A103492

Keyword

easy,nonn

Author

Harry J. Smith, Feb 08 2005

Status

approved