[math-fun] A sequence from Gardner's 6th book

Since there has been some discussion of this book, here is a sequence suggested by a problem in Chapter 4. Let S be a list of positive integers (with repeats allowed) such that every number from 1 to n can be obtained as a sum of 1 or 2 elements from S. (The minimal number of coins so that every amount from 1 through n can made using 1 or 2 coins) What are the values of a(n) = min size of any such S , for n = 1, 2, ...? (I don't know the answer.) M. G. says that a(100) <= 16, using S = { 1 3 4 5 8 14 20 26 32 38 44 47 48 49 51 52} found by Peter Wegner. NJAS