Isn't this essentially the problem discussed at http://www.stetson.edu/%7Eefriedma/mathmagic/0403.html? The table says that N(16, 2) = 104, that is, with a certain 16 denominations, at most 2 stamps (coins) can produce every value up to 104. I think the sequence you suggest can be constructed from the s = 2 column of the table. The rows d = 2,3,4,5,6 are A014616, A001208, A01209, A01210, and A01211. The columns s = 2,3,4,5,6 are A001212, A01213, A001214, A001215, A001216. This provides an explanation of these sequences, and in several cases extensions, and in the case of A001214 possibly a correction (a(8) = 220 in the OEIS and 228 in the table). ----- Original Message ----- From: N. J. A. Sloane To: math-fun@mailman.xmission.com Cc: njas@research.att.com Sent: Tuesday, June 17, 2003 12:57 AM Subject: [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 _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun