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%I A002371 M4050 N1680
%S A002371 0,1,0,6,2,6,16,18,22,28,15,3,5,21,46,13,58,60,33,35,8,13,41,44,96,4,34,
               53,
%T A002371 108,112,42,130,8,46,148,75,78,81,166,43,178,180,95,192,98,99,30,222,
%U A002371 113,228,232,7,30,50,256,262,268,5,69,28,141,146,153,155,312,79,110
%N A002371 Period of decimal expansion of 1/(n-th prime) (0 by convention for the 
               primes 2 and 5).
%C A002371 Numbers n such that A071126(n)=A000040(n)-1 - Hugo Pfoertner (hugo(AT)pfoertner.org), 
               Mar 18 2003
%C A002371 a( PrimePi[p] ) = p - 1 for prime p = {7, 17, 19, 23, 29, 47, 59, 61, 
               97, ...} = A001913(n) Cyclic numbers: primes with primitive root 
               10. a( A060257(n) ) = Prime[ A060257(n) ] - 1, where A060257(n) = 
               {4, 7, 8, 9, 10, 15, 17, 18, 25, 29, 30, 32, ...} Numbers n such 
               that 1/prime(n) has period prime(n) - 1. - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Jan 28 2007
%D A002371 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002371 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002371 Albert H. Beiler, Recreations in the Theory of Numbers, 2nd ed. New York: 
               Dover, 1966, pages 65, 309. ISBN 0-486-21096-0.
%D A002371 John H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, 
               p. 162.
%D A002371 D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 
               105, National Research Council, Washington, DC, 1941, p. 15.
%D A002371 W. Shanks, On the number of figures in the period of the reciprocal of 
               every prime number below 20 000, Proc. Royal Soc. London, 22 (1874), 
               200-210.
%H A002371 T. D. Noe, <a href="b002371.txt">Table of n, a(n) for n = 1..1000</a>
%H A002371 C. K. Caldwell, The Prime Glossary, <a href="http://primes.utm.edu/glossary/
               page.php?sort=PeriodOfAPrime">period of a prime</a>
%H A002371 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 A002371 <a href="Sindx_1.html#1overn">Index entries for sequences related to 
               decimal expansion of 1/n</a>
%e A002371 1/31 = .03225806451612903225806451612903225806452... has period 15.
%t A002371 Table[ Length[ RealDigits[1 / Prime[n]] [[1, 1]]], {n, 1, 70}]
%o A002371 (PARI) a(n)=if(n<4,n==2,znorder(Mod(10, prime(n))))
%Y A002371 See A048595 for another version. Cf. A006883, A007732, A051626, A071126, 
               A000040, A002275.
%Y A002371 Cf. A001913 = Cyclic numbers: primes with primitive root 10. Cf. A060257 
               = numbers n such that 1/prime(n) has period prime(n) - 1.
%Y A002371 Sequence in context: A126664 A011005 A021945 this_sequence A048595 A153313 
               A096050
%Y A002371 Adjacent sequences: A002368 A002369 A002370 this_sequence A002372 A002373 
               A002374
%K A002371 nonn,nice,easy
%O A002371 1,4
%A A002371 N. J. A. Sloane (njas(AT)research.att.com).
%E A002371 More terms from Arlin Anderson (starship1(AT)gmail.com)

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