id:A023416 - OEIS Search Results

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Number of 0's in binary expansion of n.

+0
97

1, 0, 1, 0, 2, 1, 1, 0, 3, 2, 2, 1, 2, 1, 1, 0, 4, 3, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 0, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 4, 3, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 0, 6, 5, 5, 4, 5, 4, 4, 3, 5, 4, 4, 3, 4, 3, 3, 2, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 5, 4, 4, 3, 4, 3, 3, 2, 4 (list; graph; listen)

	OFFSET	`0,5`
	COMMENT	`Another version (A080791) has a(0) = 0.`
	LINKS	`N. J. A. Sloane, Table of n, a(n) for n = 0..10000` `R. Stephan, Some divide-and-conquer sequences ...` `R. Stephan, Table of generating functions` `R. Stephan, Divide-and-conquer generating functions. I. Elementary sequences` `Index entries for sequences related to binary expansion of n`
	FORMULA	`a(n) = 1, if n = 0; 0, if n = 1; a(n/2)+1 if n even; a((n-1)/2) if n odd.` `a(n) = 1 - (n mod 2) + a(floor(n/2)) - Marc LeBrun (mlb(AT)well.com), Jul 12 2001` `G.f.: 1 + 1/(1-x) * Sum(k>=0, x^(2^(k+1))/(1+x^2^k)). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 15 2002`
	MATHEMATICA	`Table[ Count[ IntegerDigits[n, 2], 0], {n, 0, 100} ]`
	CROSSREFS	`The basic sequences concerning the binary expansion of n are A000120, A000788, A000069, A001969, A023416, A059015.` `a(n) = A070939(n)-A000120(n). Also A008687(n+1) - 1.` `With initial zero and shifted right, same as A080791.` `a(n) = A000120(A035327(n)).` `Sequence in context: A126258 A116382 A050606 this_sequence A080791 A124748 A119513` `Adjacent sequences: A023413 A023414 A023415 this_sequence A023417 A023418 A023419`
	KEYWORD	`nonn,nice,easy,base`
	AUTHOR	`David W. Wilson (davidwwilson(AT)comcast.net)`

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Last modified July 26 13:41 EDT 2008. Contains 142293 sequences.

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