login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A089265 a(1) = 0; thereafter a(2*n) = a(n) + 1, a(2*n+1) = 2*n. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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

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

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

PROG

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

CROSSREFS

First differences of A005766.

Cf. A003602, A220466.

Sequence in context: A058266 A138664 A140357 * A113885 A113886 A220096

Adjacent sequences:  A089262 A089263 A089264 * A089266 A089267 A089268

KEYWORD

nonn,easy

AUTHOR

Ralf Stephan, Oct 30 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 18 02:09 EST 2018. Contains 299297 sequences. (Running on oeis4.)