A007740 Period of repeating digits of 1/n in base 9.

1, 1, 1, 1, 2, 1, 3, 1, 1, 2, 5, 1, 3, 3, 2, 2, 8, 1, 9, 2, 3, 5, 11, 1, 10, 3, 1, 3, 14, 2, 15, 4, 5, 8, 6, 1, 9, 9, 3, 2, 4, 3, 21, 5, 2, 11, 23, 2, 21, 10, 8, 3, 26, 1, 10, 3, 9, 14, 29, 2, 5, 15, 3, 8, 6, 5, 11, 8, 11, 6, 35, 1, 6, 9, 10, 9, 15, 3, 39, 2, 1, 4, 41, 3, 8, 21, 14, 5, 44, 2, 3, 11, 15, 23

Offset: 1

Author

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

Keywords

• nonn
• base

Comments

Not multiplicative. Smallest counterexample a(5) = a(16) = 2, but a(80) = 2. - David W. Wilson, Jun 09 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.

Crossrefs

Cf. A007733 (base 2), A007734 (3), A007735 (4), A007736 (5), A007737 (6), A007738 (7), A007739 (8), A007732 (10).

Programs

Mathematica

DigitCycleLength[r_Rational, b_Integer?Positive] := MultiplicativeOrder[b, FixedPoint[ Quotient[#, GCD[#, b]] &, Denominator[r]]]; DigitCycleLength[1, b_Integer?Positive] = 1; Array[ DigitCycleLength[1/#, 9] &, 80] (* Robert G. Wilson v, Jun 10 2011 *)
a[n_] := MultiplicativeOrder[9, n/3^IntegerExponent[n, 3]]; Array[a, 100] (* Amiram Eldar, Aug 26 2024 *)