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

0,4

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

Formula

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

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

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 *)

Prog

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

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.

Sequence in context: A356692 A361404 A248781 * A182539 A170887 A103265

Adjacent sequences: A236837 A236838 A236839 * A236841 A236842 A236843

Keyword

nonn,base

Author

Antti Karttunen, Apr 18 2014

Status

approved