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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A106151 In binary representation of n: delete one zero in each contiguous block of zeros. 6
1, 1, 3, 2, 3, 3, 7, 4, 5, 3, 7, 6, 7, 7, 15, 8, 9, 5, 11, 6, 7, 7, 15, 12, 13, 7, 15, 14, 15, 15, 31, 16, 17, 9, 19, 10, 11, 11, 23, 12, 13, 7, 15, 14, 15, 15, 31, 24, 25, 13, 27, 14, 15, 15, 31, 28, 29, 15, 31, 30, 31, 31, 63, 32, 33, 17, 35, 18, 19, 19, 39, 20, 21, 11, 23, 22, 23 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n) <= n; a(n) = n iff n = 2^k-1: a(A000225(n))=A000225(n);

A000120(a(n))=A000120(n); A023416(a(n))=A023416(n)-A087116(n).

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences related to binary expansion of n

FORMULA

a(n) = b(n, 0), where b(n, r) = if n = 1 then 1 else b(floor(n/2), 1 - n mod 2)*(1 + floor((1 + r + n mod 2)/2)) + n mod 2.

For n <= 1, a(n) = n, and for n > 1, if n is odd, then a(n) = 1+2*a((n-1)/2), otherwise, when n is even, a(n) = (2^(A007814(n)-1)) * a(A000265(n)). - Antti Karttunen, May 13 2018

EXAMPLE

n=144 = '10010000' -> '101000' = 40 = a(144);

n=145 = '10010001' -> '101001' = 41 = a(145);

n=146 = '10010010' -> '10101' = 21 = a(146).

PROG

(Haskell)

import Data.List (group)

a106151 = foldr (\b v -> 2 * v + b) 0 . concatMap

   (\bs'@(b:bs) -> if b == 0 then bs else bs') . group . a030308_row

-- Reinhard Zumkeller, Jul 05 2013

(PARI) A106151(n) = if(n<=1, n, if(n%2, 1+(2*A106151((n-1)/2)), A106151(n>>valuation(n, 2))<<(valuation(n, 2)-1))); \\ Antti Karttunen, May 13 2018

CROSSREFS

Cf. A007088, A030308, A038573, A090078, A175047, A048679.

Sequence in context: A087713 A089319 A117231 * A323467 A239959 A214435

Adjacent sequences:  A106148 A106149 A106150 * A106152 A106153 A106154

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, May 07 2005

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 20 19:51 EDT 2019. Contains 326155 sequences. (Running on oeis4.)