# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a054471 Showing 1-1 of 1 %I A054471 #42 May 13 2024 09:16:04 %S A054471 7,3,103,53,11,79,211,41,73,281,353,37,2393,449,3061,1889,137,2467, %T A054471 16189,641,3109,4973,11087,1321,101,7151,7669,757,38629,1231,49663, %U A054471 12289,859,239,27581,9613,18131,13757,33931,9161,118901,6763,18233 %N A054471 Smallest prime p having n different cycles in decimal expansions of k/p, k=1..p-1. %C A054471 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 A054471 From _Robert G. Wilson v_, Aug 21 2014: (Start) %C A054471 recursive by indices: %C A054471 1, 7, 211, 79337, 634776923741, ... %C A054471 2, 3, 103, 2368589, 785245568161181, ... %C A054471 4, 53, 135257, 2332901103899, ... %C A054471 5, 11, 353, 3795457, 693814982285339, ... %C A054471 6, 79, 26861, 23947548497, ... %C A054471 8, 41, 118901, 1015118238709, ... %C A054471 9, 73, 142789, 267291583927, ... %C A054471 10, 281, 3097183, 66880786504811, ... %C A054471 12, 37, 18131, 105385168331, ... %C A054471 13, 2393, 11160953, ... %C A054471 ... . %C A054471 (End) %D A054471 John H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, p. 162. %D A054471 M. Gardner, Mathematical Circus, Cambridge University Press (1996). %H A054471 Robert G. Wilson v, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe) %H A054471 H. Richter, The period length of the decimal expansion of a fraction %H A054471 Index entries for sequences related to decimal expansion of 1/n %t A054471 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 A054471 First time n appears in A006556. %Y A054471 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. %Y A054471 Cf. A101208, A101209 (similar sequences for base 2 and base 3). %K A054471 nonn,easy,nice,base %O A054471 1,1 %A A054471 _Robert G. Wilson v_, 1994; Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), May 22 2000 %E A054471 More terms from _David W. Wilson_, May 22 2000 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE