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A004133 Additive bases: a(n) is the least integer such that there is an n-element set of nonnegative integers, the sums of pairs (of distinct elements) of which are distinct and at most a(n).
(Formerly M2544)
4
1, 3, 6, 11, 19, 31, 43, 63, 80, 110, 138, 169, 202, 241, 288, 330 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,2
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
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
R. L. Graham and N. J. A. Sloane, On Additive Bases and Harmonious Graphs, SIAM J. Algebraic and Discrete Methods, 1 (1980), pp. 382-404 (v_alpha).
R. L. Graham and N. J. A. Sloane, On Additive Bases and Harmonious Graphs [alternate link]
Z. Skupien, A. Zak, Pair-sums 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 131-144, (in English and Russian).
CROSSREFS
Cf. A004135, A004136. See A232234 for a slight variation.
Sequence in context: A116100 A358300 A295066 * A180415 A344003 A050228
KEYWORD
nonn,nice,more
AUTHOR
EXTENSIONS
a(11) from R. J. Mathar, Mar 17 2007
Two more terms from Jon E. Schoenfield, Aug 24 2009
202 and 241 from Skupien et al. - N. J. A. Sloane, Nov 24 2013
a(16) from Lars Blomberg, Oct 31 2015
a(17) from Fausto A. C. Cariboni, Oct 24 2017
STATUS
approved

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)