id:A090996 - OEIS Search Results

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Number of leading 1's in binary expansion of n.

+0
3

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

	OFFSET	`0,4`
	FORMULA	`a(2^k-1)=k; a(A004754(k))=1; a(A004758(k))=2.` `a(2^k-1)=k; for any other n, a(n) = a(floor(n/2)).` `a(n) = f(n, 0) with f(n, x) = if n < 2 then n + x else f([n/2], (x+1)*(n mod 2)). - Reinhard Zumkeller, Feb 02 2007`
	EXAMPLE	`In binary : 14=1110 and there are 3 leading 1's, so a(14)=3.`
	CROSSREFS	`a(n) = A007814(1+A030101(n)).` `Sequence in context: A136256 A159864 A144790 this_sequence A089309 A126387 A038374` `Adjacent sequences: A090993 A090994 A090995 this_sequence A090997 A090998 A090999`
	KEYWORD	`base,nonn`
	AUTHOR	`Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 29 2004`
	EXTENSIONS	`Edited and corrected by Frank Adams-Watters (FrankTAW(AT)Netscape.net), Apr 08 2006. Sequence had accidentally been shifted left by one step, which was corrected and term a(0)=0 added by Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Jan 01 2007.`

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Last modified November 30 13:13 EST 2009. Contains 167758 sequences.

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