login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A119920 Number of rationals in [0, 1) having exactly n preperiodic bits, then exactly n periodic bits. 0

%I #1 Sep 29 2006 03:00:00

%S 1,4,24,96,480,1728,8064,30720,129024,506880,2095104,8232960,33546240,

%T 133152768,536248320,2139095040,8589803520,34285289472,137438429184,

%U 549212651520,2198882746368,8791793860608,35184363700224

%N Number of rationals in [0, 1) having exactly n preperiodic bits, then exactly n periodic bits.

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

%e 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.

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

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

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

%K nonn,base,easy

%O 1,2

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)