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Search: id:A062050
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| A062050 |
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n-th chunk consists of numbers 1 ... 2^n. |
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+0
12
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| 1, 1, 2, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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A005836(a(n+1)) = A107681(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 20 2005
a(k) is the distance between k and the largest power of 2 not exceeding k, where k=n+1. {Consider the sequence of even numbers =<k; after sending the first term to the last position delete all odd positioned terms; the final term that remains after iterating the process is the a(k)-th even number.} - Lekraj Beedassy (blekraj(AT)yahoo.com), May 26 2005
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LINKS
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R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
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FORMULA
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a(n) = n - msb(n) + 1 (msb(n) = A053644).
a(n) = 1+floor(n-2^floor(log(n)/log(2))) - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 06 2003
G.f.: 1/(1-x) * ((1-x+x^2)/(1-x) - Sum_{k>=1} 2^(k-1)*x^2^k). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 18 2003
a(1) = 1, a(2n) = 2a(n) - 1, a(2n+1) = 2a(n). - Ralf Stephan, Oct 06 2003
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PROGRAM
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(PARI) a(n)=floor(n+1-2^floor(log2(n+1-10^-27)))
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CROSSREFS
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A053645(n) + 1.
Sequence in context: A098068 A075425 A074294 this_sequence A046653 A162190 A134292
Adjacent sequences: A062047 A062048 A062049 this_sequence A062051 A062052 A062053
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KEYWORD
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nonn
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AUTHOR
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Marc LeBrun (mlb(AT)well.com), Jun 30 2001
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EXTENSIONS
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Corrected Cloitre's formula (was off by one and using offset 0 not 1). - Joseph Biberstine (jrbibers(AT)indiana.edu), Nov 25 2008
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