A270743 Runlength sequence of the zero-one sequence A270742.

1, 1, 2, 1, 2, 4, 1, 3, 6, 1, 4, 8, 1, 5, 10, 1, 6, 12, 1, 7, 14, 1, 8, 16, 1, 9, 18, 1, 10, 20, 1, 11, 22, 1, 12, 24, 1, 13, 26, 1, 14, 28, 1, 15, 30, 1, 16, 32, 1, 17, 34, 1, 18, 36, 1, 19, 38, 1, 20, 40, 1, 21, 42, 1, 22, 44, 1, 23, 46, 1, 24, 48, 1, 25

Offset: 1

Author

Clark Kimberling, Apr 04 2016

Keywords

• nonn
• easy

Comments

This is the runlength sequence for C = (1/2)*(3/4)*(7/8)*(15/16)... in each base (2,3,4,...); for base 10, we have C = 0.8900100999989990000001000..., as in A132038.

Examples

			(zero-one sequence at A270742) = (0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,...), with first 6 runs 0, 1, 00, 1, 00, 1111 of lengths 1,1,2,1,2,4.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A132038, A270742.

Programs

Mathematica

d = Join[{0}, RealDigits[QPochhammer[1/2], 2, 200000][[1]]];
u = Map[Length, Split[d]]

Formula

a(3n) = 2n for n > 0, a(3n+1) = 1 for n >= 0, a(3n+2) = n + 1 for n >= 0.