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A119917 Number of rationals in [0, 1) consisting just of repeating bits of period at most n. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A274230 A056823 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

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Last modified January 26 11:13 EST 2020. Contains 331279 sequences. (Running on oeis4.)