A086784 - OEIS

This site is supported by donations to The OEIS Foundation.

A086784

Number of non-trailing zeros in binary representation of n.

0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 1, 0, 1, 0, 0, 0, 3, 2, 2, 1, 2, 1, 1, 0, 2, 1, 1, 0, 1, 0, 0, 0, 4, 3, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 0, 3, 2, 2, 1, 2, 1, 1, 0, 2, 1, 1, 0, 1, 0, 0, 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, 4, 3, 3, 2, 3 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,10`
	COMMENTS	`n>0: a(n) = A023416(n) - A007814(n).`
	LINKS	`Index entries for sequences related to binary expansion of n` `Eric Weisstein's World of Mathematics, Binary Carry Sequence`
	FORMULA	`a(n) = if n mod 4 = 1 then a(floor(n/4)) + A007814(floor(n/2)) else a(floor(n/2)); a(0) = a(1) = 0.`
	EXAMPLE	`a(2^n) = a(A000079(n)) = 0; a(2^n - 1) = a(A000225(n)) = 0;` `a(2^n + 1) = a(A000051(n)) = n - 1;` `n>0: a(3*2^n - 1) = a(A055010(n)) = 1;` `n>2: a(2^n - 3) = a(A036563(n)) = 1;` `a((4^n - 1)/3) = a(A002450(n)) = n.`
	CROSSREFS	`Cf. A007088.` `Sequence in context: A178471 A160381 A089311 * A104162 A145679 A007273` `Adjacent sequences: A086781 A086782 A086783 * A086785 A086786 A086787`
	KEYWORD	`nonn,base`
	AUTHOR	`Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 03 2003`

Content is available under The OEIS End-User License Agreement .

Last modified February 15 11:20 EST 2012. Contains 205773 sequences.