

A066063


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.


1



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, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12
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OFFSET

0,2


COMMENTS

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 ksubset of S covers at most binomial(k + 1, 2) members of T, we have binomial(a(n) + 1, 2) >= n + 1. It follows that A002024(n1) is a lower bound.  Rob Pratt, May 14 2004
This is an instance of the <= 2stamp postage problem with n denominations. For n > 0, a(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


LINKS

Table of n, a(n) for n=0..50.


EXAMPLE

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.


CROSSREFS

Cf. A066062, A002024, A001212.
Sequence in context: A277903 A102515 A276571 * A123087 A071868 A179390
Adjacent sequences: A066060 A066061 A066062 * A066064 A066065 A066066


KEYWORD

nonn,more


AUTHOR

John W. Layman, Dec 01 2001


EXTENSIONS

a(27)a(50) from Rob Pratt, Aug 13 2020


STATUS

approved



