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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)
+0
3
1, 3, 6, 11, 19, 31, 43, 63, 80, 110, 138, 169 (list; graph; listen)
OFFSET

2,2

COMMENT

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 (mathar(AT)strw.leidenuniv.nl), Mar 17 2007

Contribution from Jon E. Schoenfield (jonscho(AT)hiwaay.net), 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)

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

R. L. Graham and N. J. A. Sloane, On Additive Bases and Harmonious Graphs, SIAM J. Algebraic and Discrete Methods, 1 (1980), 382-404 (v_alpha).

LINKS

R. L. Graham and N. J. A. Sloane, On Additive Bases and Harmonious Graphs

CROSSREFS

Cf. A004135, A004136.

Sequence in context: A058053 A091094 A116100 this_sequence A050228 A114089 A001976

Adjacent sequences: A004130 A004131 A004132 this_sequence A004134 A004135 A004136

KEYWORD

nonn,nice,more

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

a(11) from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 17 2007

Two more terms from Jon E. Schoenfield (jonscho(AT)hiwaay.net), Aug 24 2009

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


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