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%I M4045 N1678 #43 Jun 15 2021 01:37:17
%S 1,1,6,1,2,6,16,18,6,22,3,28,15,2,3,6,5,21,46,42,16,13,18,58,60,6,33,
%T 22,35,8,6,13,9,41,28,44,6,15,96,2,4,34,53,108,3,112,6,48,22,5,42,21,
%U 130,18,8,46,46,6,42,148,75,16,78,13,66,81,166,78,18,43
%N Periods of reciprocals of integers prime to 10.
%C Nonzero terms of A084680.
%D J. W. L. Glaisher, On circulating decimals, Proc. Camb. Phil. Soc., 3 (1878), 185-206.
%D D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, pp. 7-12.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Jinyuan Wang, <a href="/A002329/b002329.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DecimalExpansion.html">Decimal Expansion</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Haupt-Exponent.html">Exponent</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MultiplicativeOrder.html">Multiplicative Order</a>
%H Chai Wah Wu, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.121.06.529">Pigeonholes and repunits</a>, Amer. Math. Monthly, 121 (2014), 529-533.
%F a(n) = A084680(A045572(n)). - _Jianing Song_, Jun 15 2021
%t Reap[ Do[ If[ CoprimeQ[n, 10], Sow[ MultiplicativeOrder[10, n]]], {n, 1, 150}]][[2, 1]] (* _Jean-François Alcover_, Nov 07 2012 *)
%o (PARI) do(lim)=my(v=List()); for(n=1, lim, if(gcd(n, 10)==1, listput(v, znorder(Mod(10,n))))); Vec(v) \\ _Charles R Greathouse IV_, Jun 21 2017
%Y Cf. A084680, A045572.
%K nonn,base,nice,easy
%O 1,3
%A _N. J. A. Sloane_
%E a(1) = 1 inserted by _Jinyuan Wang_, Jun 14 2021
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