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Search: id:A054471
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| A054471 |
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Smallest prime p having n different cycles in decimal expansions of k/p, k=1..p-1. |
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+0
4
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| 7, 3, 103, 53, 11, 79, 211, 41, 73, 281, 353, 37, 2393, 449, 3061, 1889, 137, 2467, 16189, 641, 3109, 4973, 11087, 1321, 101, 7151, 7669, 757, 38629, 1231, 49663, 12289, 859, 239, 27581, 9613, 18131, 13757, 33931, 9161, 118901, 6763, 18233
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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First cyclic number of n-th degree (or n-th order): the reciprocals of these numbers belong to one of n different cycles. Each cycle has (a(n) - 1)/n digits.
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REFERENCES
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John H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, p. 162.
M. Gardner, Mathematical Circus, Cambridge University Press (1996).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
Index entries for sequences related to decimal expansion of 1/n
H. Richter, The period length of the decimal expansion of a fraction
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MATHEMATICA
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f[n_Integer] := Block[{ds = Divisors[n - 1]}, (n - 1)/Take[ ds, Position[ PowerMod[ 10, ds, n], 1] [[1, 1]]] [[ -1]]]; t = Table[0, {50}]; Do[a = f[ Prime[n]]; If[a < 51 && t[[a]] == 0, t[[a]] = Prime[n]], {n, 2, 11225}]; t (from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 19 2005)
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CROSSREFS
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First time n appears in A006556.
Cf. A006883, A097443, A055628, A056157, A056210, A056211, A056212, A056213, A056214, A056215, A056216, A056217, A098680, which are sequences of primes p where the period of the reciprocal is (p-1)/n for n=1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13.
Sequence in context: A145758 A038269 A003723 this_sequence A086453 A112099 A013544
Adjacent sequences: A054468 A054469 A054470 this_sequence A054472 A054473 A054474
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KEYWORD
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nonn,easy,nice,base
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), 1994; Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), May 22 2000
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EXTENSIONS
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More terms from David W. Wilson (davidwwilson(AT)comcast.net), May 22, 2000.
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