A007737 Period of repeating digits of 1/n in base 6.

1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 10, 1, 12, 2, 1, 1, 16, 1, 9, 1, 2, 10, 11, 1, 5, 12, 1, 2, 14, 1, 6, 1, 10, 16, 2, 1, 4, 9, 12, 1, 40, 2, 3, 10, 1, 11, 23, 1, 14, 5, 16, 12, 26, 1, 10, 2, 9, 14, 58, 1, 60, 6, 2, 1, 12, 10, 33, 16, 11, 2, 35, 1, 36, 4, 5, 9, 10, 12, 78, 1, 1, 40, 82, 2, 16, 3, 14, 10

Offset

1,7

Comments

Not multiplicative. Smallest counterexample: a(77)=10, but a(7) = 2 and a(11) = 10. - Mitch Harris, May 16 2005.

Links

T. D. Noe, Table of n, a(n) for n=1..1000

Index entries for sequences related to decimal expansion of 1/n.

Mathematica

DigitCycleLength[r_Rational, b_Integer?Positive] := MultiplicativeOrder[b, FixedPoint[ Quotient[#, GCD[#, b]] &, Denominator[r]]]; DigitCycleLength[1, b_Integer?Positive] = 1; Array[ DigitCycleLength[1/#, 6] &, 80] (* Robert G. Wilson v, Jun 10 2011 *)
a[n_] := MultiplicativeOrder[6, n/Times @@ ({2, 3}^IntegerExponent[n, {2, 3}])]; Array[a, 100] (* Amiram Eldar, Aug 26 2024 *)

Prog

(PARI) a(n)=znorder(Mod(6, n/2^valuation(n, 2)/3^valuation(n, 3))); \\ Joerg Arndt, Dec 14 2014

Crossrefs

Cf. A007733 (base 2), A007734 (3), A007735 (4), A007736 (5), A007738 (7), A007739 (8), A007740 (9), A007732 (10).

Sequence in context: A225700 A156188 A179930 * A229243 A105688 A066017

Adjacent sequences: A007734 A007735 A007736 * A007738 A007739 A007740

Keyword

nonn,base

Author

N. J. A. Sloane, Hal Sampson (hals(AT)easynet.com)

Extensions

More terms from David W. Wilson

Status

approved