
COMMENTS

a(11) = 110 from the basis {0 1 2 4 8 15 24 29 34 46 64}. a(12)<=138 from {0 1 2 4 19 30 37 42 50 58 64 74} or {0 1 2 7 12 22 37 40 54 63 67 71} or {0 2 4 18 26 34 49 54 55 61 64 74}, for example. a(13) <= 169 from {0 1 2 5 16 30 38 47 59 65 71 78 91} or {0 1 2 5 18 28 35 50 59 65 71 79 90}. a(14) <= 202 from {0 1 2 4 7 24 38 47 56 66 74 82 95 107}. a(15) <= 250 from {0 1 2 4 13 40 61 67 83 90 98 108 113 118 132}.  R. J. Mathar, Mar 17 2007
From Jon E. Schoenfield, Aug 24 2009: (Start)
Lexicographically first basis that yields a(n) for n = 2..13:
a(2) = 1 from {0 1}
a(3) = 3 from {0 1 2}
a(4) = 6 from {0 1 2 4}
a(5) = 11 from {0 1 2 4 7}
a(6) = 19 from {0 1 2 4 7 12}
a(7) = 31 from {0 1 2 4 8 13 18}
a(8) = 43 from {0 1 2 4 8 14 19 24}
a(9) = 63 from {0 1 2 4 8 15 24 29 34}
a(10) = 80 from {0 1 2 4 8 15 24 29 34 46}
a(11) = 110 from {0 1 2 4 8 15 24 29 34 46 64}
a(12) = 138 from {0 1 2 4 19 30 37 42 50 58 64 74}
a(13) = 169 from {0 1 2 5 16 30 38 47 59 65 71 78 91}
(End)
From Lars Blomberg, Oct 31 2015: (Start)
Lexicographically first basis that yields a(n) for n=14..16:
a(14) = 202 from {0,1,2,4,7,24,38,47,56,66,74,82,95,107}
a(15) = 241 from {0,1,2,22,26,36,43,50,82,90,95,98,101,113,128}
a(16) = 288 from {0,4,5,10,31,43,55,58,92,100,111,120,122,129,136,152}
(End)
Lexicographically first basis that yields a(17) = 330 is {0,5,9,10,11,43,62,75,88,112,115,129,136,143,151,159,171}.  Fausto A. C. Cariboni, Oct 24 2017


LINKS

Table of n, a(n) for n=2..17.
R. L. Graham and N. J. A. Sloane, On Additive Bases and Harmonious Graphs, SIAM J. Algebraic and Discrete Methods, 1 (1980), 382404 (v_alpha).
R. L. Graham and N. J. A. Sloane, On Additive Bases and Harmonious Graphs
Z. Skupien, A. Zak, Pairsums packing and rainbow cliques, in Topics In Graph Theory, A tribute to A. A. and T. E. Zykovs on the occasion of A. A. Zykov's 90th birthday, ed. R. Tyshkevich, Univ. Illinois, 2013, pages 131144, (in English and Russian).
