A103496 Multiplicative suborder of 10 (mod 2n+1) = sord(10, 2n+1).

0, 1, 0, 3, 1, 1, 3, 0, 8, 9, 6, 11, 0, 3, 14, 15, 2, 0, 3, 6, 5, 21, 0, 23, 21, 16, 13, 0, 18, 29, 30, 6, 0, 33, 22, 35, 4, 0, 3, 13, 9, 41, 0, 28, 22, 3, 15, 0, 48, 2, 2, 17, 0, 53, 54, 3, 56, 0, 6, 48, 11, 5, 0, 21, 21, 65, 9, 0, 4, 23, 46, 3, 0, 42, 74, 75, 16, 0, 39, 13, 33, 81, 0, 83, 39

Offset

0,4

Comments

a(n) is minimum e for which 10^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..84.

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[10, 2 n + 1];
a /@ Range[0, 100] (* Jean-François Alcover, Mar 21 2020, after T. D. Noe in A003558 *)

Crossrefs

Sequence in context: A218489 A218332 A322506 * A345441 A267863 A262681

Adjacent sequences: A103493 A103494 A103495 * A103497 A103498 A103499

Keyword

easy,nonn

Author

Harry J. Smith, Feb 11 2005

Status

approved