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 A079302 #20 Apr 22 2025 09:48:05 %S A079302 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2,0,3,0,0,0,1,2,0,0,18,0,13,0,0, %T A079302 0,0,0,6,5,2,0,3,6,0,0,0,0,37,0,1,2,0,3,34,0,17,0,25,44,4,0,15,32,7,0, %U A079302 0,0,0,0,3,0,244,0,7,13,2,8,0,6,129,0,3,6 %N A079302 a(n) = number of shortest addition chains for n that are non-Brauer chains. %C A079302 In a general addition chain, each element > 1 is a sum of two previous elements (the two may be the same element). In a Brauer chain, each element > 1 is a sum of the immediately previous element and another previous element. Conversely, a non-Brauer chain has at least one element that is the sum of two elements earlier than the preceding one. %H A079302 Glen Whitney, <a href="/A079302/b079302.txt">Table of n, a(n) for n = 1..18286</a> (Terms 1..1024 from D. W. Wilson) %H A079302 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BrauerChain.html">Brauer Chain.</a> %H A079302 Glen Whitney, <a href="https://oeis.org/A079300/a079300.c.txt">C program to compute A079300</a>, also generates this sequence. %e A079302 7 has five shortest addition chains: (1,2,3,4,7), (1,2,3,5,7), (1,2,3,6,7), (1,2,4,5,7), and (1,2,4,6,7). All of these are Brauer chains. Hence a(7) = 0. %e A079302 13 has ten shortest addition chains: (1,2,3,5,8,13), (1,2,3,5,10,13), (1,2,3,6,7,13), (1,2,3,6,12,13), (1,2,4,5,9,13), (1,2,4,6,7,13), (1,2,4,6,12,13), (1,2,4,8,9,13), (1,2,4,8,12,13), and (1,2,4,5,8,13). Of these, only the last is non-Brauer. Hence a(13) = 1. %e A079302 12509 has 28 shortest addition chains, all of which happen to be non-Brauer (in fact, it is the smallest natural number for which all shortest addition chains are non-Brauer). Hence a(12509) = A079300(12509) = 28. %Y A079302 Cf. A079300, the total number of minimal addition chains. %K A079302 nonn %O A079302 1,19 %A A079302 _David W. Wilson_, Feb 09 2003 %E A079302 Definition disambiguated by _Glen Whitney_, Nov 06 2021