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A119918 Table read by antidiagonals: number of rationals in [0, 1) having exactly n preperiodic bits, then exactly k periodic bits (read up antidiagonals). 2
1, 1, 2, 2, 2, 6, 4, 4, 6, 12, 8, 8, 12, 12, 30, 16, 16, 24, 24, 30, 54, 32, 32, 48, 48, 60, 54, 126, 64, 64, 96, 96, 120, 108, 126, 240, 128, 128, 192, 192, 240, 216, 252, 240, 504, 256, 256, 384, 384, 480, 432, 504, 480, 504, 990, 512, 512, 768, 768, 960, 864, 1008 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..62.

FORMULA

a(n, k) = 2^max{0, n-1} * sum_{d|k} (2^d - 1) * mu(k/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, 2) = |{1/12 = 0.00(01)..., 5/12 = 0.01(10)..., 7/12 = 0.10(01)..., 11/12 = 0.11(10)...}| = 4

Table begins:

1 2 6 12

1 2 6 12

2 4 12 24

4 8 24 48

MATHEMATICA

Table[2^ Max[0, n-1](Plus@@((2^Divisors[k]-1)MoebiusMu[k/Divisors[k]])), {n, 0, 1 0}, {k, 1, 10}]

CROSSREFS

Outer product of A011782 and A038199.

Sequence in context: A210550 A208659 A209752 * A084867 A194949 A227550

Adjacent sequences:  A119915 A119916 A119917 * A119919 A119920 A119921

KEYWORD

nonn,base,easy,tabl

AUTHOR

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

STATUS

approved

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Last modified September 16 11:05 EDT 2019. Contains 327095 sequences. (Running on oeis4.)