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A086799 Replace all trailing 0's with 1's in binary representation of n. 10
1, 3, 3, 7, 5, 7, 7, 15, 9, 11, 11, 15, 13, 15, 15, 31, 17, 19, 19, 23, 21, 23, 23, 31, 25, 27, 27, 31, 29, 31, 31, 63, 33, 35, 35, 39, 37, 39, 39, 47, 41, 43, 43, 47, 45, 47, 47, 63, 49, 51, 51, 55, 53, 55, 55, 63, 57, 59, 59, 63, 61, 63, 63, 127, 65, 67, 67, 71, 69, 71 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) = n + 2^A007814(n) - 1;

a(n) is odd; a(n) = n iff n is odd;

a(a(n)) = a(n); A007814(a(n)) = a(n); A000265(a(n)) = a(n);

A023416(a(n)) = A023416(n) - A007814(n) = A086784(n);

A000120(a(n)) = A000120(n) + A007814(n);

a(2^n) = a(A000079(n)) = 2*2^n - 1 = A000051(n+1).

a(n) = A006519(n) + n - 1. - Reinhard Zumkeller, Feb 02 2007

a(k+1) = smallest number greater than k having in binary representation exactly one 1 more than k has; A000120(a(n)) = A063787(n). - Reinhard Zumkeller, Jul 31 2010

a(2*n) = A038712(n) + 2*n. - Reinhard Zumkeller, Aug 07 2011

a(n) is the least m >= n-1, such that the Hamming distance D(n-1,m) = 1. - Vladimir Shevelev, Apr 18 2012

LINKS

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

R. Stephan, Some divide-and-conquer sequences ...

R. Stephan, Table of generating functions

Eric Weisstein's World of Mathematics, Binary Carry Sequence

Eric Weisstein's World of Mathematics, Odd Part

Index entries for sequences related to binary expansion of n

FORMULA

a(n) = if n is odd then n else a(n/2)*2 + 1.

a(n) = n OR n-1 (bitwise OR of consecutive numbers). - Russ Cox, May 15 2007

a((2*n-1)*2^p) = 2^(p+1)*n-1, p >= 0. - Johannes W. Meijer, Feb 01 2013

EXAMPLE

a(20) = a('10100') = '10100' + '11' = '10111' = 23.

MAPLE

nmax:=70: 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) := 2^(p+1)*n-1 od: od: seq(a(n), n=1..nmax); # Johannes W. Meijer, Feb 01 2013

MATHEMATICA

Table[BitOr[(n + 1), n], {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 19 2011 *)

PROG

(C:) int a(int n) { return n | (n-1); } // Russ Cox, May 15 2007

(Haskell)

a086799 n | even n    = (a086799 $ div n 2) * 2 + 1

          | otherwise = n

-- Reinhard Zumkeller, Aug 07 2011

(PARI) a(n)=bitor(n, n-1) \\ Charles R Greathouse IV, Apr 17 2012

CROSSREFS

Cf. A007088, A179857, A220466.

Sequence in context: A137695 A318456 A209085 * A218388 A161427 A098688

Adjacent sequences:  A086796 A086797 A086798 * A086800 A086801 A086802

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Aug 05 2003

STATUS

approved

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Last modified October 17 07:05 EDT 2018. Contains 316276 sequences. (Running on oeis4.)