Oban Number

By way of analogy with the eban numbers, oban numbers are defined as numbers whose English names do not contain the letter "o" (i.e., "o" 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 large numbers.

The first few are 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 23, 25, 26, ... (OEIS A008521).

Since the number name for every power of 10 greater than 3 contains either "thousand" or the suffix "-illion", there are a finite number of oban numbers. In fact, there are a total of 454 of them, the largest of which is 999.

A plot of the oban numbers represented as a sequence of binary bits is shown above.

REFERENCES:

Sloane, N. J. A. Sequence A008521 in "The On-Line Encyclopedia of Integer Sequences."