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A126235 Minimum length of a codeword in Huffman encoding of n symbols, where the k-th symbol has frequency k. 3
1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,4

REFERENCES

M. J. Fisher et al., The birank number of a graph, Congressus Numerant., 204 (2010), 173-180.

LINKS

Table of n, a(n) for n=2..103.

Wikipedia, Article on Huffman coding

FORMULA

Conjecture: a(n) = A099396(n+1) = floor(log2(2(n+1)/3)) where 'log2' means the logarithm to the base 2. Equivalently, a(n)-a(n-1)=1 if n has the form 3*2^k-1 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 shortest codewords have length a(8)=2.

CROSSREFS

Cf. A099396, A126014 and A126237. The maximum length of a codeword is in A126236.

Sequence in context: A081604 A123119 A099396 * A220104 A191228 A286103

Adjacent sequences:  A126232 A126233 A126234 * A126236 A126237 A126238

KEYWORD

nonn

AUTHOR

Dean Hickerson, Dec 21 2006

STATUS

approved

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Last modified March 4 08:38 EST 2021. Contains 341781 sequences. (Running on oeis4.)