This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A119921 #3 Jun 30 2025 20:01:45
%S A119921 2,12,72,336,1632,6720,29568,120576,499200,2012160,8214528,32894976,
%T A119921 132882432,532070400,2136637440,8551464960,34282536960,137135652864,
%U A119921 549148164096,2196721631232,8791208755200,35166005231616
%N A119921 Number of rationals in [0, 1) having at most n preperiodic bits, then at most n periodic bits.
%F A119921 a(n) = 2^n * sum_{j=1..n} sum_{d|j} (2^d - 1) * mu(j/d)
%e A119921 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 A119921 a(2) = |{ 0/1 = 0.(0)..., 1/3 = 0.(01)..., 2/3 = 0.(10)..., 1/2 = 0.1(0)..., 1/6 = 0.0(01)..., 5/6 = 0.1(10)..., 1/4 = 0.01(0)..., 3/4 = 0.11(0)..., 1/12 = 0.00(01)..., 5/12 = 0.01(10)..., 7/12 = 0.10(01)..., 11/12 = 0.11(10)...}| = 12
%t A119921 Table[2^n Sum[Plus@@((2^Divisors[j]-1)MoebiusMu[j/Divisors[j]]),{j,1,n}],{n,1,22}]
%Y A119921 Elementwise product of 2^n (offset 1) and A119917. Also, diagonal of A119919.
%K A119921 nonn,base,easy
%O A119921 1,1
%A A119921 Brad Chalfan (brad(AT)chalfan.net), May 28 2006