|
%I #21 Aug 13 2020 22:11:46
%S 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,
%T 10,10,10,10,10,10,10,11,11,11,11,11,11,12,12,12,12
%N 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.
%C 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.
%C Since each k-subset 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(n-1) is a lower bound. - _Rob Pratt_, May 14 2004
%C This is an instance of the <= 2-stamp 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
%e 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.
%Y Cf. A066062, A002024, A001212.
%K nonn,more
%O 0,2
%A _John W. Layman_, Dec 01 2001
%E a(27)-a(50) from _Rob Pratt_, Aug 13 2020
|
