A119917 Number of rationals in [0, 1) consisting just of repeating bits of period at most n.

1, 3, 9, 21, 51, 105, 231, 471, 975, 1965, 4011, 8031, 16221, 32475, 65205, 130485, 261555, 523131, 1047417, 2094957, 4191975, 8384229, 16772835, 33545715, 67100115, 134200785, 268418001, 536837061, 1073707971, 2147415981

Offset: 1

Author

Brad Chalfan (brad(AT)chalfan.net), May 29 2006

Keywords

• nonn
• base
• easy

Examples

			1/6 = 0.0010101... has repeating bits of period 2, but is not counted because it has a preperiodic part (i.e., the repetition doesn't start immediately after the binary point). Also, 0 = 0.000... is counted and considered to have period 1.
a(1) = |{0 = 0.(0)...}| = 1
a(2) = |{0 = 0.(0)..., 1/3 = 0.(01)..., 2/3 = 0.(10)...}| = 3
		

Crossrefs

Partial sums of A038199.

Programs

Mathematica

Table[Sum[Plus@@((2^Divisors[i]-1)MoebiusMu[i/Divisors[i]]),{i,1,n}],{n,1,30 }]

Formula

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