This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A126235 #15 Nov 14 2024 14:16:22 %S A126235 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, %T A126235 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, %U A126235 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 %N A126235 Minimum length of a codeword in Huffman encoding of n symbols, where the k-th symbol has frequency k. %H A126235 M. J. Fisher et al., <a href="https://drive.google.com/file/d/1VOM9IqzgOM1xZeq_KpDcpYRsvDLAa8iV/view">The birank number of a graph</a>, Congressus Numerant., 204 (2010), 173-180. %H A126235 Wikipedia, <a href="http://en.wikipedia.org/wiki/Huffman_coding">Huffman coding</a> %F A126235 Conjecture: a(n) = A099396(n+1) = floor(log_2(2(n+1)/3)). Equivalently, a(n) = a(n-1) + 1 if n has the form 3*2^k-1, a(n) = a(n-1) otherwise. This is true at least for n up to 1000. %e A126235 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. %Y A126235 Cf. A099396, A126014 and A126237. The maximum length of a codeword is in A126236. %K A126235 nonn %O A126235 2,4 %A A126235 _Dean Hickerson_, Dec 21 2006