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A119920 Number of rationals in [0, 1) having exactly n preperiodic bits, then exactly n periodic bits. 0
1, 4, 24, 96, 480, 1728, 8064, 30720, 129024, 506880, 2095104, 8232960, 33546240, 133152768, 536248320, 2139095040, 8589803520, 34285289472, 137438429184, 549212651520, 2198882746368, 8791793860608, 35184363700224 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..23.

FORMULA

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

EXAMPLE

The binary expansion of 7/24 = 0.010(01)... has 3 preperiodic bits (to the right of the binary point) followed by 2 periodic (i.e., repeating) bits, while 1/2 = 0.1(0)... has one bit of each type. The preperiodic and periodic parts are both chosen to be as short as possible.

a(2) = |{1/12 = 0.00(01)..., 5/12 = 0.01(10)..., 7/12 = 0.10(01)..., 11/12 = 0.11(10)...}| = 4

MATHEMATICA

Table[2^(n-1)(Plus@@((2^Divisors[n]-1)MoebiusMu[n/Divisors[n]])), {n, 1, 23} ]

CROSSREFS

Elementwise product of 2^n (offset 0) and A038199. Also, diagonal of A119918.

Sequence in context: A100381 A319793 A091143 * A100738 A139238 A139231

Adjacent sequences:  A119917 A119918 A119919 * A119921 A119922 A119923

KEYWORD

nonn,base,easy

AUTHOR

Brad Chalfan (brad(AT)chalfan.net), May 28, 2006

STATUS

approved

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Last modified January 28 12:58 EST 2020. Contains 331321 sequences. (Running on oeis4.)