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%I #14 Mar 21 2020 16:36:46
%S 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,
%T 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,
%U 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
%N Multiplicative suborder of 6 (mod 2n+1) = sord(6, 2n+1).
%C a(n) is minimum e for which 6^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[6, 2 n + 1];
%t a /@ Range[0, 100] (* _Jean-François Alcover_, Mar 21 2020, after _T. D. Noe_ in A003558 *)
%K easy,nonn
%O 0,6
%A _Harry J. Smith_, Feb 11 2005
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