Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #14 Mar 21 2020 16:37:14
%S 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,
%T 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,
%U 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
%N Multiplicative suborder of 10 (mod 2n+1) = sord(10, 2n+1).
%C a(n) is minimum e for which 10^e = +/-1 mod 2n+1, or zero if no e exists.
%D H. Cohen, Course in Computational Algebraic Number Theory, Springer, 1993, p. 25, Algorithm 1.4.3
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MultiplicativeOrder.html">Multiplicative Order.</a>
%H S. Wolfram, <a href="http://www.stephenwolfram.com/publications/articles/ca/84-properties/9/text.html">Algebraic Properties of Cellular Automata (1984)</a>, Appendix B.
%t Suborder[k_, n_] := If[n > 1 && GCD[k, n] == 1, Min[MultiplicativeOrder[k, n, {-1, 1}]], 0];
%t a[n_] := Suborder[10, 2 n + 1];
%t a /@ Range[0, 100] (* _Jean-François Alcover_, Mar 21 2020, after _T. D. Noe_ in A003558 *)
%K easy,nonn
%O 0,4
%A _Harry J. Smith_, Feb 11 2005