|
| |
|
|
A033264
|
|
Number of blocks of {1,0} in the binary expansion of n.
|
|
11
|
|
|
|
0, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 2, 1, 2, 2, 3, 2, 3, 3, 3, 2, 2, 2, 3, 2, 2, 2, 2, 1, 1, 1, 2, 1, 2, 2, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,10
|
|
|
COMMENTS
|
Number of i such that d(i)<d(i-1), where Sum{d(i)*2^i: i=0,1,....,m} is base 2 representation of n.
|
|
|
LINKS
|
_Reinhard Zumkeller_, Table of n, a(n) for n = 1..10000
R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
Eric Weisstein's World of Mathematics, Digit Block
|
|
|
FORMULA
|
G.f.: 1/(1-x) * sum(k>=0, t^2/(1+t)/(1+t^2), t=x^2^k). - Ralf Stephan, Sep 10 2003
a(n) = A069010(n) - (n mod 2). - Ralf Stephan, Sep 10 2003
a(4n) = a(4n+1) = a(2n), a(4n+2) = a(n)+1, a(4n+3) = a(n). - Ralf Stephan, Aug 20 2003
|
|
|
PROG
|
(Haskell)
import Data.List (tails, isPrefixOf)
a033264 = sum . map (fromEnum . ([0, 1] `isPrefixOf`)) .
tails . a030308_row
-- Reinhard Zumkeller, Jun 17 2012
|
|
|
CROSSREFS
|
Cf. A014081, A014082, A037800, A056974, A056975, A056976, A056977, A056978, A056979, A056980.
a(n) = A005811(n) - ceiling(A005811(n)/2) = A005811(n) - A069010(n).
Equals (A072219(n+1)-1)/2.
Cf. A175047, A087116. [From Reinhard Zumkeller, Dec 12 2009]
Cf. A030308.
Sequence in context: A047988 A037818 A087116 * A080234 A136049 A225192
Adjacent sequences: A033261 A033262 A033263 * A033265 A033266 A033267
|
|
|
KEYWORD
|
nonn,base,easy
|
|
|
AUTHOR
|
Clark Kimberling
|
|
|
STATUS
|
approved
|
| |
|
|
