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Search: id:A160824
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| A160824 |
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a(1)=1. a(n) = the smallest positive integer such that both a(n) and sum{k=1 to n} a(k) have the same number of (nonleading) 0's when they are represented in binary. |
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+0
2
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| 1, 5, 1, 6, 9, 4, 18, 8, 36, 16, 72, 32, 144, 64, 288, 128, 576, 256, 1152, 512, 2304, 1024, 4608, 2048, 9216, 4096, 18432, 8192, 36864, 16384, 73728, 32768, 147456, 65536, 294912, 131072, 589824, 262144, 1179648, 524288, 2359296, 1048576, 4718592
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Sum{k=1 to n} a(k) = A160825(n).
Consider the related sequence {b(k)}, where b(1) = 1, b(n) = the smallest positive integer such that both b(n) and sum{k=1 to n} b(k) have the same number of 1's when they are represented in binary. Then b(1) = 1, and b(n) = 2^(n-2), for all n >= 2. (b(n) = A011782(n-1).)
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FORMULA
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a(2n) = 2^(n-1) and a(2n-1) = 9*2^(n-3) for n >= 3 (cf. formula for A160825). - Hagen von Eitzen (math(AT)von-eitzen.de), Jun 01 2009
G.f.: (-8*x^5 + 7*x^4 - 4*x^3 - x^2 + 5*x + 1)/(-2*x^2 + 1) [From Alexander R. Povolotsky (pevnev(AT)juno.com), Jun 08 2009]
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CROSSREFS
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Cf. A160825.
Sequence in context: A131944 A058651 A164105 this_sequence A007397 A052345 A111008
Adjacent sequences: A160821 A160822 A160823 this_sequence A160825 A160826 A160827
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), May 27 2009
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jun 15 2009
Edited by N. J. A. Sloane, Jul 31 2009 at the suggestion of R. J. Mathar
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