

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
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OFFSET

1,2


LINKS

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


FORMULA

a(n) = 2^(n1) * sum_{dn} (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^(n1)(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



