A236840 n minus number of runs in the binary expansion of n: a(n) = n - A005811(n).

0, 0, 0, 2, 2, 2, 4, 6, 6, 6, 6, 8, 10, 10, 12, 14, 14, 14, 14, 16, 16, 16, 18, 20, 22, 22, 22, 24, 26, 26, 28, 30, 30, 30, 30, 32, 32, 32, 34, 36, 36, 36, 36, 38, 40, 40, 42, 44, 46, 46, 46, 48, 48, 48, 50, 52, 54, 54, 54, 56, 58, 58, 60, 62, 62, 62, 62, 64, 64, 64

Offset: 0

Author

Antti Karttunen, Apr 18 2014

Keywords

• nonn
• base

Comments

All terms are even. Used by the "number-of-runs beanstalk" sequence A255056 and many of its associated sequences.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8192

Crossrefs

Cf. A091067 (the positions of records), A106836 (run lengths).

Cf. A255070 (terms divided by 2).

Cf. A005811, A000120, A003188.

Cf. A255056, A255066, A255061, A255062, A255071, A255072, A255058, A255327.

Other subtracting maps: A011371, A178503, A219641, A219651, A227190, A227191, A237449, A244320, A244234, A255131.

Programs

Maple

A236840 := proc(n) local i, b; if n=0 then 0 else b := convert(n, base, 2); select(i -> (b[i-1]<>b[i]), [$2..nops(b)]); n-1-nops(%) fi end: seq(A236840(i), i=0..69); # Peter Luschny, Apr 19 2014

Mathematica

a[n_] := n - Length@ Split[IntegerDigits[n, 2]]; a[0] = 0; Array[a, 100, 0] (* Amiram Eldar, Jul 16 2023 *)

Scheme

(define (A236840 n)  (- n (A005811 n)))

Formula

a(n) = n - A005811(n) = n - A000120(A003188(n)).

a(n) = 2*A255070(n).