A002329 Periods of reciprocals of integers prime to 10.

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, 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, 130, 18, 8, 46, 46, 6, 42, 148, 75, 16, 78, 13, 66, 81, 166, 78, 18, 43

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• nice
• easy

Comments

Nonzero terms of A084680.

References

• J. W. L. Glaisher, On circulating decimals, Proc. Camb. Phil. Soc., 3 (1878), 185-206.
• D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, pp. 7-12.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Jinyuan Wang, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Decimal Expansion.
• Eric Weisstein's World of Mathematics, Exponent.
• Eric Weisstein's World of Mathematics, Multiplicative Order
• Chai Wah Wu, Pigeonholes and repunits, Amer. Math. Monthly, 121 (2014), 529-533.

Crossrefs

Cf. A084680, A045572.

Programs

Mathematica

Reap[ Do[ If[ CoprimeQ[n, 10], Sow[ MultiplicativeOrder[10, n]]], {n, 1, 150}]][[2, 1]] (* Jean-François Alcover, Nov 07 2012 *)

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

Formula

a(n) = A084680(A045572(n)). - Jianing Song, Jun 15 2021

Extensions

a(1) = 1 inserted by Jinyuan Wang, Jun 14 2021