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%I #39 Mar 02 2019 02:40:26
%S 7,3,103,53,11,79,211,41,73,281,353,37,2393,449,3061,1889,137,2467,
%T 16189,641,3109,4973,11087,1321,101,7151,7669,757,38629,1231,49663,
%U 12289,859,239,27581,9613,18131,13757,33931,9161,118901,6763,18233
%N Smallest prime p having n different cycles in decimal expansions of k/p, k=1..p-1.
%C 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.
%C From _Robert G. Wilson v_, Aug 21 2014: (Start)
%C recursive by indices:
%C 1, 7, 211, 79337, 634776923741, ...
%C 2, 3, 103, 2368589, 785245568161181, ...
%C 4, 53, 135257, 2332901103899, ...
%C 5, 11, 353, 3795457, 693814982285339, ...
%C 6, 79, 26861, 23947548497, ...
%C 8, 41, 118901, 1015118238709, ...
%C 9, 73, 142789, 267291583927, ...
%C 10, 281, 3097183, 66880786504811, ...
%C 12, 37, 18131, 105385168331, ...
%C 13, 2393, 11160953, ...
%C ... .
%C (End)
%D John H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, p. 162.
%D M. Gardner, Mathematical Circus, Cambridge University Press (1996).
%H Robert G. Wilson v, <a href="/A054471/b054471.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)
%H H. Richter, <a href="http://hr.userweb.mwn.de/numb/period.html">The period length of the decimal expansion of a fraction</a>
%H <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n</a>
%t 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 *)
%Y First time n appears in A006556.
%Y 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.
%K nonn,easy,nice,base
%O 1,1
%A _Robert G. Wilson v_, 1994; Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), May 22 2000
%E More terms from _David W. Wilson_, May 22 2000
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