A002329 Periods of reciprocals of integers prime to 10. (Formerly M4045 N1678)

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

1,3

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.

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A084680, A045572.

Sequence in context: A216415 A112828 A085766 * A053453 A347197 A156792

Adjacent sequences: A002326 A002327 A002328 * A002330 A002331 A002332

Keyword

nonn,base,nice,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved