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A054471 Smallest prime p having n different cycles in decimal expansions of k/p, k=1..p-1. 8
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; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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.
From Robert G. Wilson v, Aug 21 2014: (Start)
recursive by indices:
1, 7, 211, 79337, 634776923741, ...
2, 3, 103, 2368589, 785245568161181, ...
4, 53, 135257, 2332901103899, ...
5, 11, 353, 3795457, 693814982285339, ...
6, 79, 26861, 23947548497, ...
8, 41, 118901, 1015118238709, ...
9, 73, 142789, 267291583927, ...
10, 281, 3097183, 66880786504811, ...
12, 37, 18131, 105385168331, ...
13, 2393, 11160953, ...
... .
(End)
REFERENCES
John H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, p. 162.
M. Gardner, Mathematical Circus, Cambridge University Press (1996).
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
MATHEMATICA
f[n_Integer] := Block[{k = 1, p}, While[p = k*n + 1; ! PrimeQ[p] || p != 1 + n*MultiplicativeOrder[10, p] || GCD[10, p] > 1, k++]; p]; Array[f, 50] (* Robert G. Wilson v, Apr 19 2005; revised Aug 20 2014 *)
CROSSREFS
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: A173443 A003723 A241438 * A086453 A320842 A112099
KEYWORD
nonn,easy,nice,base
AUTHOR
Robert G. Wilson v, 1994; Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), May 22 2000
EXTENSIONS
More terms from David W. Wilson, May 22 2000
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)