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 A079301 a(n) = number of shortest addition chains for n that are Brauer chains. 10

%I #20 Nov 09 2021 05:39:59

%S 1,1,1,1,2,2,5,1,3,4,15,3,9,14,4,1,2,7,31,6,26,40,4,4,13,22,5,23,114,

%T 12,64,1,2,4,43,12,33,87,18,8,20,78,4,69,14,8,183,5,11,34,4,35,171,16,

%U 139,32,148

%N a(n) = number of shortest addition chains for n that are Brauer chains.

%C In a general addition chain, each element > 1 is a sum of two previous elements. In a Brauer chain, each element > 1 is a sum of the immediately previous element and another previous element.

%H Glen Whitney, <a href="/A079301/b079301.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="/A079300/a079300.c.txt">C program to compute A079300</a>, also generates this sequence.

%e All five of the shortest addition chains for 7 are Brauer chains: (1,2,3,4,7), (1,2,3,5,7), (1,2,3,6,7), (1,2,4,5,7), (1,2,4,6,7). Hence a(7) = 5.

%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, all but the last are Brauer chains. Hence a(13) = 9.

%e 12509 has 28 shortest addition chains, none of which are Brauer chains. Hence a(12509) = 0.

%K nonn

%O 1,5

%A _David W. Wilson_, Feb 09 2003

%E Definition disambiguated by _Glen Whitney_, Nov 06 2021

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Last modified October 4 02:45 EDT 2023. Contains 365872 sequences. (Running on oeis4.)