A103492 Multiplicative suborder of 6 (mod 2n+1) = sord(6, 2n+1).

0, 0, 1, 1, 0, 5, 6, 0, 8, 9, 0, 11, 5, 0, 7, 3, 0, 2, 2, 0, 20, 3, 0, 23, 7, 0, 13, 10, 0, 29, 30, 0, 12, 33, 0, 35, 18, 0, 5, 39, 0, 41, 16, 0, 44, 12, 0, 9, 6, 0, 5, 51, 0, 53, 54, 0, 56, 11, 0, 16, 55, 0, 25, 63, 0, 65, 18, 0, 68, 23, 0, 60, 14, 0, 37, 75, 0, 6, 78, 0, 22, 27, 0, 83, 78, 0, 43

Offset

0,6

Comments

a(n) is minimum e for which 6^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..86.

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[6, 2 n + 1];
a /@ Range[0, 100] (* Jean-François Alcover, Mar 21 2020, after T. D. Noe in A003558 *)

Crossrefs

Sequence in context: A194347 A021869 A340319 * A344476 A362529 A200010

Adjacent sequences: A103489 A103490 A103491 * A103493 A103494 A103495

Keyword

easy,nonn

Author

Harry J. Smith, Feb 11 2005

Status

approved