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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
38
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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)lhsystems.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).
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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