id:A023416 - OEIS Search Results

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Number of 0's in binary expansion of n.

+0
109

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 A161225` `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 November 27 14:34 EST 2009. Contains 167570 sequences.

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