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%I A001913 M4353 N1823
%S A001913 7,17,19,23,29,47,59,61,97,109,113,131,149,167,179,181,193,223,229,233,
%T A001913 257,263,269,313,337,367,379,383,389,419,433,461,487,491,499,503,509,541,
%U A001913 571,577,593,619,647,659,701,709,727,743,811,821,823,857,863,887,937,941
%N A001913 Cyclic numbers: primes with primitive root 10.
%C A001913 Primes p such that the decimal expansion of 1/p has period p-1.
%C A001913 Primes p such that the corresponding entry in A002371 is p-1.
%C A001913 Pieter Moree writes (Oct 20 2004): Assuming the Generalized Riemann Hypothesis 
               it can be shown that the density of primes p such that a prescribed 
               integer g has order (p-1)/t, with t fixed exists and, moreover, it 
               can be computed. This density will be a rational number times the 
               so called Artin constant. For 2 and 10 the density of primitive roots 
               is A, the Artin constant itself.
%C A001913 R. K. Guy writes (Oct 20 2004): MR 2004j:11141 speaks of the unearthing 
               by Lenstra & Stevenhagen of correspondence concerning the density 
               of this sequence between the Lehmers & Artin.
%C A001913 Primes p such that the decimal expansion of 1/p has period p-1, which 
               is the greatest period possible for any integer.
%D A001913 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, 1964 (and various 
               reprintings), p. 864.
%D A001913 Albert H. Beiler, Recreations in the Theory of Numbers, 2nd ed. New York: 
               Dover, 1966, pages 65, 309.
%D A001913 John H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, 
               p. 161.
%D A001913 L. J. Goldstein, Density questions in algebraic number theory, Amer. 
               Math. Monthly, 78 (1971), 342-349.
%D A001913 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 
               3rd ed., Oxford Univ. Press, 1954, p. 115.
%D A001913 M. Kraitchik, Recherches sur la Th\'{e}orie des Nombres. Gauthiers-Villars, 
               Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 61.
%D A001913 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001913 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A001913 T. D. Noe, <a href="b001913.txt">Table of n, a(n) for n=1..1000</a>
%H A001913 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A001913 B. Chanco, <a href="http://bchanco.free.fr/frp/ArtinIntro.html">Full 
               Reptend Prime</a>
%H A001913 Pieter Moree, <a href="http://turing.wins.uva.nl/~moree/varia.htm">Artin's 
               primitive root conjecture - a survey</a>
%H A001913 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CyclicNumber.html">Link to a section of The World of Mathematics.</
               a>
%H A001913 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DecimalExpansion.html">Link to a section of The World of Mathematics.</
               a>
%H A001913 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               FullReptendPrime.html">Link to a section of The World of Mathematics.</
               a>
%H A001913 D. Williams, <a href="http://www.louisville.edu/~dawill03/crypto/Primitive.html">
               Primitive Roots (Check)</a>
%H A001913 <a href="Sindx_Pri.html#primes_root">Index entries for primes by primitive 
               root</a>
%H A001913 <a href="Sindx_1.html#1overn">Index entries for sequences related to 
               decimal expansion of 1/n</a>
%t A001913 f[n_]:=Block[{q},q=Last[First[RealDigits[1/n]]];If[IntegerQ[q],q={}];
               FromDigits[q]]; q=0;lst={};Do[If[StringLength[ToString[f[n]]]>q,AppendTo[lst,
               n];q=StringLength[ToString[f[n]]]],{n,6!}];lst [From Vladimir Orlovsky 
               (4vladimir(AT)gmail.com), May 21 2009]
%t A001913 pr=10; Select[Prime[Range[200]], MultiplicativeOrder[pr, # ] == #-1 &]
%Y A001913 Apart from initial term, identical to A006883.
%Y A001913 Other definitions of cyclic numbers: A003277, A001914. Cf. A005596, A001122, 
               A048296.
%Y A001913 Sequence in context: A101240 A058887 A167797 this_sequence A071845 A084704 
               A156005
%Y A001913 Adjacent sequences: A001910 A001911 A001912 this_sequence A001914 A001915 
               A001916
%K A001913 nonn,easy,nice
%O A001913 1,1
%A A001913 N. J. A. Sloane (njas(AT)research.att.com).

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