OFFSET
1,5
COMMENTS
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.
LINKS
Glen Whitney, Table of n, a(n) for n = 1..18286 (Terms 1..1024 from D. W. Wilson)
Eric Weisstein's World of Mathematics, Brauer Chain
Glen Whitney, C program to compute A079300, also generates this sequence.
EXAMPLE
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.
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.
12509 has 28 shortest addition chains, none of which are Brauer chains. Hence a(12509) = 0.
CROSSREFS
KEYWORD
nonn
AUTHOR
David W. Wilson, Feb 09 2003
EXTENSIONS
Definition disambiguated by Glen Whitney, Nov 06 2021
STATUS
approved