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

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, 308, 33, 24, 76, 201, 80, 1, 2, 4, 23, 6, 26, 134, 1014

Offset: 1

Author

David W. Wilson, Feb 09 2003

Keywords

• nonn

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.

Examples

			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.
		

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.

Extensions

Definition disambiguated by Glen Whitney, Nov 06 2021