A089265 a(1) = 0; thereafter a(2*n) = a(n) + 1, a(2*n+1) = 2*n.

0, 1, 2, 2, 4, 3, 6, 3, 8, 5, 10, 4, 12, 7, 14, 4, 16, 9, 18, 6, 20, 11, 22, 5, 24, 13, 26, 8, 28, 15, 30, 5, 32, 17, 34, 10, 36, 19, 38, 7, 40, 21, 42, 12, 44, 23, 46, 6, 48, 25, 50, 14, 52, 27, 54, 9, 56, 29, 58, 16, 60, 31, 62, 6, 64, 33, 66, 18, 68, 35, 70, 11, 72

Offset: 1

Author

Ralf Stephan, Oct 30 2003

Keywords

• nonn
• easy

Comments

In the binary representation of n, swallow all zeros from the right, then add the number of swallowed zeros, and subtract 1. - Ralf Stephan, Aug 22 2013

Links

• T. D. Noe, Table of n, a(n) for n=1..1000
• Index entries for sequences related to binary expansion of n

Crossrefs

First differences of A005766.

Cf. A003602, A220466.

Programs

Maple

nmax:=73: for p from 0 to ceil(simplify(log[2](nmax))) do for n from 1 to ceil(nmax/(p+2)) do a((2*n-1)*2^p) := p  + 2*(n-1) od: od: seq(a(n), n=1..nmax); # Johannes W. Meijer, Jan 23 2013

Mathematica

a[n_] := With[{v = IntegerExponent[n, 2]}, v + n/2^v - 1];
Array[a, 100] (* Jean-François Alcover, Feb 28 2019 *)

PARI

a(n) = valuation(n,2) + n/2^valuation(n,2) - 1

Formula

a(1) = 0; thereafter a(2*n) = a(n) + 1, a(2*n+1) = 2*n.

a(n) = A007814(n) + 2*A025480(n-1) = A007814(n) + A000265(n) - 1.

G.f.: sum(k>=0, (t^2+2t^3-t^4)/(1-t^2)^2, t=(x^2)^k).

a((2*n-1)*2^p) = p + 2*(n-1), p >= 0. - Johannes W. Meijer, Jan 23 2013