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A086799
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Replace all trailing 0's by 1's in binary representation of n.
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10
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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_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
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FORMULA
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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
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EXAMPLE
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a(20) = a('10100') = '10100' + '11' = '10111' = 23.
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MAPLE
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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]
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MATHEMATICA
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Table[BitOr[(n + 1), n], {n, 0, 100}] (* From Vladimir Joseph Stephan Orlovsky, Jul 19 2011 *)
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PROG
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(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
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CROSSREFS
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Cf. A007088, A179857, A220466
Sequence in context: A205680 A137695 A209085 * A218388 A161427 A098688
Adjacent sequences: A086796 A086797 A086798 * A086800 A086801 A086802
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KEYWORD
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nonn,base
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AUTHOR
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Reinhard Zumkeller, Aug 05 2003
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STATUS
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approved
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