id:A086784 - OEIS Search Results

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

+0
4

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; listen)

	OFFSET	`0,10`
	COMMENT	`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.` `Adjacent sequences: A086781 A086782 A086783 this_sequence A086785 A086786 A086787` `Sequence in context: A125753 A057516 A089311 this_sequence A104162 A007273 A016319`
	KEYWORD	`nonn,base`
	AUTHOR	`Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 03 2003`

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Last modified October 9 14:06 EDT 2008. Contains 144831 sequences.

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