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A007733
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Period of binary representation of 1/n.
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10
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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, 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, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| 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
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
Contribution from John W. Layman (layman(AT)math.vt.edu), Jan 22 2009: (Start)
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).
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)
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REFERENCES
| 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.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
Index entries for sequences related to decimal expansion of 1/n
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FORMULA
| a(n) = A002326( (A000265(n)-1)/2 ) [From Max Alekseyev (maxale(AT)gmail.com), Jun 11 2009]
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MATHEMATICA
| f[n_] := MultiplicativeOrder[2, n/(2^IntegerExponent[n, 2])]; Array[f, 84] (* Robert G. Wilson v, June 10 2011 *)
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CROSSREFS
| Cf. A136042 [From John W. Layman (layman(AT)math.vt.edu), Jan 22 2009]
Sequence in context: A078458 A033317 A183200 * A128520 A123755 A118291
Adjacent sequences: A007730 A007731 A007732 * A007734 A007735 A007736
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Hal Sampson [hals(AT)easynet.com]
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