%I A007733
%S A007733 1,1,2,1,4,2,3,1,6,4,10,2,12,3,4,1,8,6,18,4,6,10,11,2,20,12,18,3,28,4,
               5,
%T A007733 1,10,8,12,6,36,18,12,4,20,6,14,10,12,11,23,2,21,20,8,12,52,18,20,3,18,
%U A007733 28,58,4,60,5,6,1,12,10,66,8,22,12,35,6,9,36,20,18,30,12,39,4,54,20,82,
               6
%N A007733 Period of binary representation of 1/n.
%C A007733 Also sequence of period lengths for n's when you do primality testing 
               and calculate "2^k mod n" from k=0 to k=n - Gottfried Helms (helms(AT)uni-kassel.de), 
               Oct 05 2000
%C A007733 Fractal sequence related to A002326: the even terms of this sequence 
               are this sequence itself, constructed on A002326, whose terms are 
               the odd terms of this sequence. - Alexandre Wajnberg (alexandre.wajnberg(AT)ulb.ac.be), 
               Apr 27 2005
%C A007733 Contribution from John W. Layman (layman(AT)math.vt.edu), Jan 22 2009: 
               (Start)
%C A007733 It seems that a(n) is also the sum of the terms in one period of the 
               base-2 MR-expansion of 1/n (see A136042 for definition).
%C A007733 a(n) appears to be the multiplicative order of 2 modulo the odd part 
               of n (the largest odd divisor of n). This has been verified up to 
               n=2000 for the base-2 MR-expansion interpretation. (End)
%D A007733 Simmons, G. J. The structure of the differentiation digraphs of binary 
               sequences. Ars Combin. 35 (1993), A, 71-88, see Table 2. Math. Rev. 
               95f:05052.
%H A007733 <a href="Sindx_1.html#1overn">Index entries for sequences related to 
               decimal expansion of 1/n</a>
%F A007733 a(n) = A002326( (A000265(n)-1)/2 ) [From Max Alekseyev (maxale(AT)gmail.com), 
               Jun 11 2009]
%Y A007733 A136042 [From John W. Layman (layman(AT)math.vt.edu), Jan 22 2009]
%Y A007733 Sequence in context: A130584 A078458 A033317 this_sequence A128520 A123755 
               A118291
%Y A007733 Adjacent sequences: A007730 A007731 A007732 this_sequence A007734 A007735 
               A007736
%K A007733 nonn,easy
%O A007733 1,3
%A A007733 N. J. A. Sloane (njas(AT)research.att.com), Hal Sampson [ hals(AT)easynet.com 
               ]