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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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6
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 31 2010]
a(2*n) = A038712(n) + 2*n. [Reinhard Zumkeller, Aug 07 2011]
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LINKS
| 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
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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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 (rsc(AT)swtch.com), May 15 2007
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EXAMPLE
| a(20) = a('10100') = '10100' + '11' = '10111' = 23.
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MATHEMATICA
| Table[BitOr[(n + 1), n], {n, 0, 100}] (* From Vladimir Joseph Stephan Orlovsky, Jul 19 2011 *)
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PROG
| (C:) int a(int n) { return n | (n-1); } - Russ Cox (rsc(AT)swtch.com), May 15 2007
(Haskell)
a086799 n | even n = (a086799 $ div n 2) * 2 + 1
| otherwise = n
-- Reinhard Zumkeller, Aug 07 2011
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CROSSREFS
| Cf. A007088.
Cf. A179857. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 31 2010]
Sequence in context: A118362 A205680 A137695 * A161427 A098688 A129266
Adjacent sequences: A086796 A086797 A086798 * A086800 A086801 A086802
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 05 2003
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