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%I #16 Nov 09 2021 15:03:27
%S 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 0,0,0,6,5,2,0,3,6,0,0,0,0,37,0,1,2,0,3,34,0,17,0,25
%N a(n) = number of shortest addition chains for n that are non-Brauer chains.
%C 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 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BrauerChain.html">Brauer Chain.</a>
%H Glen Whitney, <a href="https://oeis.org/A079300/a079300.c.txt">C program to compute A079300</a>, also generates this sequence.
%e 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 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 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 Cf. A079300, the total number of minimal addition chains.
%K nonn
%O 1,19
%A _David W. Wilson_, Feb 09 2003
%E Definition disambiguated by _Glen Whitney_, Nov 06 2021
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