id:A126236 - OEIS Search Results

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Maximum length of a codeword in Huffman encoding of n symbols, where the k-th symbol has frequency k.

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4

1, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11 (list; graph; listen)

	OFFSET	`2,2`
	LINKS	`Wikipedia, Article on Huffman coding`
	FORMULA	`Conjecture: a(n) = floor(log2(n)) + floor(log2(2n/3)) where 'log2' means the logarithm to the base 2. Equivalently, a(n)-a(n-1)=1 if n has the form 2^k or 3*2^k and =0 otherwise. This is true at least for n up to 1000.`
	EXAMPLE	`A Huffman code for n=8 is (1->00000, 2->00001, 3->0001, 4->001, 5->010, 6->011, 7->10, 8->11). The longest codewords have length a(8)=5.`
	CROSSREFS	`Cf. A126014 and A126237. The minimum length of a codeword is in A126235.` `Sequence in context: A130500 A072073 A061716 this_sequence A073047 A038567 A036234` `Adjacent sequences: A126233 A126234 A126235 this_sequence A126237 A126238 A126239`
	KEYWORD	`nonn`
	AUTHOR	`Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 21 2006`

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Last modified December 21 10:15 EST 2009. Contains 171081 sequences.

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