If the members of the set :
S={2^x3^y : x>=0,y>=0}
are arranged in increasing order we get the sequence beginning
1,2,3,4,6,8,9,12,16,18,......
(a)What is the position of 2^a3^b in the sequence in terms of a and b.
(b)What is the n-th term of the sequence in terms of n.

The sequence, with discussion, can be found at A003586 in Sloane's OEIS.

Posted by Charlie on 2013-09-09 09:47:10