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Search: id:A006556
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| A006556 |
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Number of different cycles of digits in the decimal expansions of 1/p, 2/p, ..., (p-1)/p where p = n-th prime different from 2 or 5.
(Formerly M0175)
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+0
5
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| 2, 1, 5, 2, 1, 1, 1, 1, 2, 12, 8, 2, 1, 4, 1, 1, 2, 2, 9, 6, 2, 2, 1, 25, 3, 2, 1, 1, 3, 1, 17, 3, 1, 2, 2, 2, 1, 4, 1, 1, 2, 1, 2, 2, 7, 1, 2, 1, 1, 34, 8, 5, 1, 1, 1, 54, 4, 10, 2, 2, 2, 2, 1, 4, 3, 1, 2, 3, 11, 2, 1, 2, 1, 1, 1, 4, 2, 2, 1, 3, 2, 1, 2, 2, 14, 3, 1, 3, 2, 2, 1, 1, 1, 1, 1, 10, 2, 1, 6
(list; graph; listen)
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OFFSET
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3,1
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REFERENCES
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J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 162.
M. Kraitchik, Recherches sur la Th\'{e}orie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 131.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n=3..1000
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FORMULA
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(p-1)/x, where 10^x = 1 mod p.
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EXAMPLE
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1/13=.0769230769..., 2/13=.1538461538..., 3/13= .2307692307..., etc., with 2 different cycles, so a(4) = 2 [13 is the 4th prime different from 2 or 5].
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CROSSREFS
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See A048595 and A002371 for the length of the cycles. See also A054471.
Sequence in context: A119763 A092142 A140879 this_sequence A108790 A117941 A134566
Adjacent sequences: A006553 A006554 A006555 this_sequence A006557 A006558 A006559
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KEYWORD
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nonn,easy,base,nice,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 24 2000
Edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Nov 01 2009
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