%I A000000 %S A000000 1,1,1,1,2,2,5,1,3,4,15,3,10,14,4,1,2,7,33,6,29,40,4,4,14,24,5,23,132,12,77, %T A000000 1,2,4,43,12,39,92,20,8,23,84,4,69,14,8,220,5,12,36,4,38,205,16,156,32,173 %N A000000 Number of minimal addition chains for n. %e A000000 7 has a(7) = 5 minimal addition 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). %H A000000 E. W. Weisstein, Link to a section of The World of Mathematics. %Y A000000 Cf. A000001, A000002 %K A000000 nonn %O A000000 1,5 %A A000000 David W Wilson (davidwwilson@attbi.com) %I A000001 %S A000001 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, %T A000001 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 %N A000001 Number of minimal Brauer chains for n. %C A000001 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. %e A000001 7 has a(7) = 5 minimal 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). %H A000001 E. W. Weisstein, Link to a section of The World of Mathematics. %Y A000000 Cf. A000000, A000002 %K A000001 nonn %O A000001 1,5 %A A000001 David W Wilson (davidwwilson@attbi.com) %I A000002 %S A000002 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, %T A000002 0,0,6,5,2,0,3,6,0,0,0,0,37,0,1,2,0,3,34,0,17,0,25 %N A000002 Number of minimal non-Brauer chains for n. %C A000002 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. %e A000002 13 has a(13) = 1 minimal non-Brauer chain: (1,2,4,5,8,13). %H A000002 E. W. Weisstein, Link to a section of The World of Mathematics. %Y A000000 Cf. A000000, A000001 %K A000002 nonn %O A000002 1,19 %A A000002 David W Wilson (davidwwilson@attbi.com)