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%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
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