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Search: id:A053644
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| A053644 |
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Most significant bit of n, msb(n); largest power of 2 less than or equal to n; write n in binary and change all but the first digit to zero. |
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+0
41
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| 0, 1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Except for the initial term, 2^n appears 2^n times. - Lekraj Beedassy (blekraj(AT)yahoo.com), May 26 2005
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LINKS
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N. J. A. Sloane, Transforms
R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
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FORMULA
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a(n) = a(floor(n / 2)) * 2.
a(n)=2^A000523(n)
a(0)=0, a(1)=1 and a(n+1)=a(n)*floor(n/a(n)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 17 2002
G.f.: 1/(1-x) * (x + sum_{k>=1} 2^(k-1)*x^2^k). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 18 2003
a(n) = (A003817(n)+1)/2 = A091940(n)+1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 15 2004
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CROSSREFS
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See A000035 for least significant bit(n).
MASKTRANS transform of A055975 (prepended with 0), MASKTRANSi transform of A048678.
From n >= 1 onward, A053644[n] = A062383[n]/2
Bisection of A065267, A065279, A065291, A072376.
First differences of A063915. Cf. A076877, A073121.
This is Guy Steele's sequence GS(5, 5) (see A135416).
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 2009: (Start)
Equals for n>=1 the first right hand column of A160464.
(End)
Sequence in context: A098667 A105678 A028397 this_sequence A039593 A101656 A090557
Adjacent sequences: A053641 A053642 A053643 this_sequence A053645 A053646 A053647
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KEYWORD
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easy,nonn,nice
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Mar 22 2000
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