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Fix e = 3; a(n) = minimal Hamming distance between the binary representation of n and the binary representation of any multiple ke (0 <= k <= n/e) which is a child of n.

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0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 2, 1, 0, 1, 1, 0, 1, 2, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 2, 1, 0, 1, 1, 0, 2, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1 (list; graph; listen)

	OFFSET	`0,6`
	COMMENT	`A number m is a child of n if the binary representation of n has a 1 in every position where the binary representation of m has a 1.` `In other words, this tells us how closely (in Hamming weight) we can approximate n "from below" by a multiple of e.`
	LINKS	`Nadia Heninger and N. J. A. Sloane, Table of n, a(n) for n = 0..5000` `N. J. A. Sloane, Fortran program for this and related sequences`
	EXAMPLE	`If n = 14 = 1110_2, take k=2, ke = 6 = 110_2, which is Hamming distance 1 from n. This is the best we can do, so a(14) = 1.`
	PROGRAM	`See link for Fortran program.`
	CROSSREFS	`For e=2 and 4 through 9 see A000035 and A140081 through A140086.` `Cf. A140137, A140138, A140200-A140206.` `Sequence in context: A025886 A117355 A086966 this_sequence A065359 A087372 A036431` `Adjacent sequences: A140077 A140078 A140079 this_sequence A140081 A140082 A140083`
	KEYWORD	`nonn`
	AUTHOR	`Nadia Heninger (nadiah(AT)cs.princeton.edu) and njas, Jun 03 2008`

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Last modified December 3 10:07 EST 2008. Contains 151162 sequences.

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