A007735 Period of base 4 representation of 1/n.

1, 1, 1, 1, 2, 1, 3, 1, 3, 2, 5, 1, 6, 3, 2, 1, 4, 3, 9, 2, 3, 5, 11, 1, 10, 6, 9, 3, 14, 2, 5, 1, 5, 4, 6, 3, 18, 9, 6, 2, 10, 3, 7, 5, 6, 11, 23, 1, 21, 10, 4, 6, 26, 9, 10, 3, 9, 14, 29, 2, 30, 5, 3, 1, 6, 5, 33, 4, 11, 6, 35, 3, 9, 18, 10, 9, 15, 6, 39, 2, 27, 10, 41, 3, 4, 7, 14, 5, 11, 6, 6, 11, 5

Offset: 1

Author

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

Keywords

• nonn
• base

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), A007736 (5), A007737 (6), A007738 (7), A007739 (8), A007740 (9), 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/#, 4] &, 80] (* Robert G. Wilson v, Jun 10 2011 *)
a[n_] := MultiplicativeOrder[4, n/2^IntegerExponent[n, 2]]; Array[a, 100] (* Amiram Eldar, Aug 26 2024 *)

Extensions

More terms from David W. Wilson