Isn't this essentially the problem discussed
at
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 -----
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
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