(OEIS A051037). The name refers to a problem attributed to R. W. Hamming of generating these numbers in increasing order
without duplicates (Dijkstra 1976, pp. 129-134).
The sequence can be generated in increasing order without duplicates by starting with 1 and merging three copies of it scaled by 2, 3, and
5, retaining equal values only once (Dijkstra 1981).
Dijkstra, E. W. "An Exercise Attributed to R. W. Hamming." Ch. 17 in A
Discipline of Programming. Englewood Cliffs, NJ: Prentice-Hall, pp. 129-134,
1976.Dijkstra, E. W. "Hamming's Exercise in SASL." EWD792,
1981. https://www.cs.utexas.edu/~EWD/ewd07xx/EWD792.PDF.Sloane,
N. J. A. Sequence A051037 in "The
On-Line Encyclopedia of Integer Sequences."
,
, and 
are nonnegative integers.
Equivalently, the Hamming numbers are the 5-smooth numbers.
They begin
