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 A079302 a(n) = number of shortest addition chains for n that are non-Brauer chains. 6
 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, 0, 0, 0, 6, 5, 2, 0, 3, 6, 0, 0, 0, 0, 37, 0, 1, 2, 0, 3, 34, 0, 17, 0, 25 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,19 COMMENTS 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. 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 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. 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. 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. CROSSREFS Cf. A079300, the total number of minimal addition chains. Sequence in context: A080300 A116864 A255308 * A138806 A181105 A142971 Adjacent sequences: A079299 A079300 A079301 * A079303 A079304 A079305 KEYWORD nonn AUTHOR David W. Wilson, Feb 09 2003 EXTENSIONS Definition disambiguated by Glen Whitney, Nov 06 2021 STATUS approved

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Last modified September 24 00:14 EDT 2023. Contains 365554 sequences. (Running on oeis4.)