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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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45
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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; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Except for the initial term, 2^n appears 2^n times. - Lekraj Beedassy, May 26 2005
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LINKS
| N. J. A. Sloane, Transforms
R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
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FORMULA
| 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, Aug 17 2002
G.f.: 1/(1-x) * (x + sum_{k>=1} 2^(k-1)*x^2^k). - Ralf Stephan, Apr 18 2003
a(n) = (A003817(n)+1)/2 = A091940(n)+1. - Reinhard Zumkeller, Feb 15 2004
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MATHEMATICA
| a[n_] := 2^(Length[ IntegerDigits[n, 2]] - 1); a[0] = 0; Table[a[n], {n, 0, 74}] (* From Jean-François Alcover, Dec 01 2011 *)
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PROG
| (Haskell)
a053644 n = a053644_list !! n
a053644_list = 0 : concat (rep 0) where
rep n = (replicate (2^n) (2^n)) : rep (n+1)
-- Reinhard Zumkeller, Oct 21 2011, Oct 17 2010
(PARI) a(n)=my(k=1); while(k<=n, k<<=1); k>>1 \\ Charles R Greathouse IV, May 27 2011
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CROSSREFS
| 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).
Equals for n>=1 the first right hand column of A160464. - Johannes W. Meijer, May 24 2009
Diagonal of A088370. - Alois P. Heinz, Oct 28 2011
Sequence in context: A098667 A105678 A028397 * A039593 A101656 A090557
Adjacent sequences: A053641 A053642 A053643 * A053645 A053646 A053647
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KEYWORD
| easy,nonn,nice
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Mar 22 2000
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