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%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