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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 The first 1000 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 A112099 A013324 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 December 11 15:03 EST 2018. Contains 318049 sequences. (Running on oeis4.)