By way of analogy with the eban numbers, uban numbers are defined as numbers whose English names do not contain the letter "u" (i.e., "u" is banned). Note that this definition is imprecise insofar as special names are sometimes assigned to a few large numbers that do not follow the usual rules for the naming of such numbers.

The first few uban numbers are 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, ... (OEIS A089590). The sequence of uban numbers first differs from OEIS A052406 (the numbers not containing the digit 4) at the term 40 (forty), which is a uban number but is not 4-less.

A plot of the first few uban numbers represented as a sequence of binary bits is shown above. The top portion shows the first 255 values, and the bottom shows the next 510 values.

REFERENCES:

Sloane, N. J. A. Sequences A052406 and A089590 in "The On-Line Encyclopedia of Integer Sequences."