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Search: id:A066063
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| A066063 |
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Size of the smallest subset S of T={0,1,2,...,n} such that each element of T is the sum of two elements of S. |
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+0
2
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| 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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If one counts all subsets S of T={0,1,2,...n} such that each number in T is the sum of two elements of S, sequence A066062 is obtained.
Since each k-subset of S covers at most binom(k + 1, 2) members of T, we have binom(A066063(n) + 1, 2) >= n + 1. It follows that A002024(n-1) is a lower bound. - Rob Pratt (Rob.Pratt(AT)sas.com), May 14 2004
This is an instance of the <= 2-stamp postage problem with n denominations. For n > 0, A066063(n) = 1 + the smallest i such that A001212(i) >= n (adding one adjusts for the fact that A001212 has offset 1). - Tim Peters (tim.one(AT)comcast.net), Aug 25 2006
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EXAMPLE
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For n=2, it is clear that S={0,1} is the unique subset of {0,1,2} that satisfies the definition, so a(2)=2.
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CROSSREFS
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A066062
Cf. A002024.
Cf. A001212.
Sequence in context: A137397 A062571 A102515 this_sequence A123087 A071868 A082447
Adjacent sequences: A066060 A066061 A066062 this_sequence A066064 A066065 A066066
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Dec 01 2001
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