id:A069010 - OEIS Search Results

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Number of runs of 1's in binary representation of n.

+0
6

0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 2, 2, 2, 3, 2, 2, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 2, 2, 2, 3, 2, 2, 2, 3, 3, 3, 2, 3, 2, 2, 1, 2, 2, 2, 2, 3, 2, 2, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 2, 2, 2, 3, 2, 2, 2, 3, 3, 3, 2, 3, 2, 2, 2, 3, 3, 3, 3, 4, 3, 3, 2, 3, 3, 3, 2, 3 (list; graph; listen)

	OFFSET	`0,6`
	LINKS	`R. Stephan, Some divide-and-conquer sequences ...` `R. Stephan, Table of generating functions`
	FORMULA	`a(n) =ceiling[A005811(n)/2] =A005811(n)-A033264(n). If 2^k<=n<32^(k-1) then a(n)=a(n-2^k)+1; if 32^(k-1)<=n<2^(k+1) then a(n)=a(n-2^k).` `a(2n) = a(n), a(2n+1) = a(n) + [n is even]. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Aug 20 2003` `G.f.: 1/(1-x) * sum(k>=0, t/(1+t)/(1+t^2), t=x^2^k). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 07 2003` `a(n) = A000120(n) - A014081(n) = A037800(n) + 1, n>0. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 10 2003`
	EXAMPLE	`a(11)=2 since 11 is 1011 in binary with two runs of 1's. a(12)=1 since 12 is 1100 in binary with one run of 1's.`
	CROSSREFS	`Sequence in context: A029364 A122586 A079487 this_sequence A087048 A109700 A087742` `Adjacent sequences: A069007 A069008 A069009 this_sequence A069011 A069012 A069013`
	KEYWORD	`base,easy,nonn`
	AUTHOR	`Henry Bottomley (se16(AT)btinternet.com), Apr 02 2002`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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