5-smooth number

A 5-smooth number, also called a Hamming number, is a positive integer of the form $2^a{3}^b{5}^c$ with $a,b,c\ge 0$. The sequence begins $1,2,3,4,5,6,8,9,10,12,15,16,18,20,\dots$.

The number seven is absent, while arbitrarily large powers of two are present. To generate the sequence in increasing order, merge the three sorted sequences formed by multiplying earlier values by $2,3,5$, removing duplicates. For a finite bound $B$, an equivalent search enumerates exponent triples satisfying $a\log 2+b\log 3+c\log 5\le \log B$.