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%I #14 Mar 21 2020 16:37:07
%S 0,0,1,0,1,1,0,3,1,0,1,5,0,3,3,0,2,4,0,9,2,0,5,11,0,5,3,0,3,7,0,15,4,
%T 0,4,6,0,9,9,0,2,2,0,21,5,0,11,23,0,21,5,0,3,13,0,10,3,0,7,29,0,5,15,
%U 0,8,6,0,11,8,0,6,35,0,3,9,0,9,15,0,39,2,0,2,41,0,8,21,0,5,22,0,3,11,0,23
%N Multiplicative suborder of 9 (mod n) = sord(9, n).
%C a(n) is minimum e for which 9^e = +/-1 mod n, 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[9, n];
%t a /@ Range[0, 100] (* _Jean-François Alcover_, Mar 21 2020, after _T. D. Noe_ in A003558 *)
%K easy,nonn
%O 0,8
%A _Harry J. Smith_, Feb 08 2005