5-smooth number
= 5-smooth number
= Hamming number
{c}
{synonym}
= Ugly number
{synonym}
= 5-smooth
{synonym}
A <5-smooth number>, also called a <Hamming number>, is a positive <integer> of the form $2^a3^b5^c$ with $a,b,c\ge0$. The <sequence> begins $1,2,3,4,5,6,8,9,10,12,15,16,18,20,\ldots$.
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 $a\log2+b\log3+c\log5\le\log B$.