Search: id:A003558
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%I A003558
%S A003558 0,1,2,3,3,5,6,4,4,9,6,11,10,9,14,5,5,12,18,12,10,7,12,23,21,8,26,20,9,
%T A003558 29,30,6,6,33,22,35,9,20,30,39,27,41,8,28,11,12,10,36,24,15,50,51,12,53,
%U A003558 18,36,14,44,12,24,55,20,50,7,7,65,18,36,34,69,46,60,14,42,74,15,24,20
%N A003558 Least number m such that 2^m = +- 1 mod 2n + 1.
%C A003558 Multiplicative suborder of 2 (mod 2n+1) (or sord(2, 2n+1)).
%C A003558 For the complexity of computing this, see A002326.
%C A003558 It appears that under iteration of the base-n Kaprekar map, for even 
               n > 2 (A165012, A165051, A165090, A151949 in bases 4, 6, 8, 10), 
               almost all cycles are of length a(n/2 - 1); proved under the additional 
               constraint that the cycle contains at least one element satisfying 
               "number of digits (n-1) - number of digits 0 = o(total number of 
               digits)". [From Joseph Myers (jsm(AT)polyomino.org.uk), Sep 05 2009]
%D A003558 H. Cohen, Course in Computational Algebraic Number Theory, Springer, 
               1993, p. 25, Algorithm 1.4.3
%D A003558 V. I. Levenshtein, Conflict-avoiding codes and cyclic triple systems 
               [in Russian], Problemy Peredachi Informatsii, 43 (No. 3, 2007), 39-53.
%H A003558 T. D. Noe, <a href="b003558.txt">Table of n, a(n) for n = 0..1000</a>
%H A003558 H. J. Smith, <a href="http://harry-j-smith.com/hjsmithh/download.html#XICalc">
               XICalc - Extra Precision Integer Calculator.</a>
%H A003558 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               MultiplicativeOrder.html">Link to a section of The World of Mathematics</
               a>, Multiplicative Order.
%H A003558 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.
%H A003558 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SuborderFunction.html">Math World: Suborder Function</a>
%t A003558 Suborder[a_,n_] := If[n>1 && GCD[a,n]==1, Min[MultiplicativeOrder[a,n,
               {-1,1}]],0]; Table[Suborder[2,2n+1], {n,0,100}] - T. D. Noe (noe(AT)sspectra.com), 
               Aug 02 2006
%Y A003558 a(n) = log_2(A160657(n) + 2) - 1 [From Nathaniel Johnston (nathaniel(AT)nathanieljohnston.com), 
               May 22 2009]
%Y A003558 Sequence in context: A023160 A085312 A046530 this_sequence A141419 A072451 
               A023156
%Y A003558 Adjacent sequences: A003555 A003556 A003557 this_sequence A003559 A003560 
               A003561
%K A003558 nonn
%O A003558 0,3
%A A003558 N. J. A. Sloane (njas(AT)research.att.com).
%E A003558 More terms from Harry J. Smith (hjsmithh(AT)sbcglobal.net), Feb 11 2005
%E A003558 Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Aug 02 2006

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