A103493 Multiplicative suborder of 7 (mod n) = sord(7, n).

0, 0, 1, 1, 1, 2, 1, 0, 1, 3, 2, 5, 2, 6, 0, 4, 2, 8, 3, 3, 4, 0, 5, 11, 2, 2, 6, 9, 0, 7, 4, 15, 4, 10, 8, 0, 6, 9, 3, 12, 4, 20, 0, 3, 5, 12, 11, 23, 2, 0, 2, 16, 12, 13, 9, 20, 0, 3, 7, 29, 4, 30, 15, 0, 8, 6, 10, 33, 16, 22, 0, 35, 6, 12, 9, 4, 6, 0, 12, 39, 4, 27, 20, 41, 0, 16, 3, 7, 5, 44, 12

Offset

0,6

Comments

a(n) is minimum e for which 7^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..90.

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

Crossrefs

Sequence in context: A078806 A173438 A376701 * A121480 A082601 A286509

Adjacent sequences: A103490 A103491 A103492 * A103494 A103495 A103496

Keyword

easy,nonn

Author

Harry J. Smith, Feb 08 2005

Status

approved