A119917 Number of rationals in [0, 1) consisting just of repeating bits of period at most n.

1, 3, 9, 21, 51, 105, 231, 471, 975, 1965, 4011, 8031, 16221, 32475, 65205, 130485, 261555, 523131, 1047417, 2094957, 4191975, 8384229, 16772835, 33545715, 67100115, 134200785, 268418001, 536837061, 1073707971, 2147415981

Offset

1,2

Links

Table of n, a(n) for n=1..30.

Formula

a(n) = sum_{i=1..n} sum_{d|i} (2^d - 1) * mu(i/d)

Example

1/6 = 0.0010101... has repeating bits of period 2, but is not counted because it has a preperiodic part (i.e., the repetition doesn't start immediately after the binary point). Also, 0 = 0.000... is counted and considered to have period 1.
a(1) = |{0 = 0.(0)...}| = 1
a(2) = |{0 = 0.(0)..., 1/3 = 0.(01)..., 2/3 = 0.(10)...}| = 3

Mathematica

Table[Sum[Plus@@((2^Divisors[i]-1)MoebiusMu[i/Divisors[i]]), {i, 1, n}], {n, 1, 30 }]

Crossrefs

Partial sums of A038199.

Sequence in context: A056823 A369343 A105544 * A111209 A262444 A109755

Adjacent sequences: A119914 A119915 A119916 * A119918 A119919 A119920

Keyword

nonn,base,easy

Author

Brad Chalfan (brad(AT)chalfan.net), May 29, 2006

Status

approved