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 A054471 Smallest prime p having n different cycles in decimal expansions of k/p, k=1..p-1. 7
 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 Adjacent sequences:  A054468 A054469 A054470 * A054472 A054473 A054474 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 October 20 10:45 EDT 2019. Contains 328257 sequences. (Running on oeis4.)