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 A079301 a(n) = number of shortest addition chains for n that are Brauer chains. 10
 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, 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, 139, 32, 148 (list; graph; refs; listen; history; text; internal format)
 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 Sequence in context: A173169 A016586 A073690 * A079300 A128932 A286150 Adjacent sequences: A079298 A079299 A079300 * A079302 A079303 A079304 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 May 28 22:21 EDT 2023. Contains 363028 sequences. (Running on oeis4.)