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There are several variations of ban numbers.

Aban numbers

Aban numbers are defined as numbers that do not contain the letter 'a' when spelled in English. This definition is not definitive as some large numbers do not follow the guidelines for naming of numbers.

From this definition, one understands that numbers including the word "thousand" are not aban numbers, but all smaller numbers are. The first aban numbers are: 1-999, 1000000-1000999, 2000000-2000999, ... etc.

The letter 'a' in the word 'and' is not considered.
Eban numbers

Eban numbers are defined as numbers who don't contain the letter 'e' when spelled in English. This definition is not definitive as some large numbers don't follow the guidelines for naming of numbers. The name of this term was created by Neil James Alexander Sloane in 1990.

Because every odd number contains an e, the first eban numbers are: 2, 4, 6, 30, 32, 34, 36, 40, 42, 44, 46, 50, 52, 54, 56, 60, 62, 64, 66, 2000, 2002, 2004, ...

Some properties concern eban numbers:

A gap larger than any given number can be found between two eban numbers
Let an eban number be of the form \( 2\cdot 10^k \) then \( 2\cdot 10^k+2 \) is also an eban number for \( k\in N \)

Iban numbers

Iban numbers are defined as numbers who don't contain the letter 'i' when spelled in English. This definition is not definitive as some large numbers don't follow the guidelines for naming of numbers e.g. googol and googolplex.

The first iban numbers are 1, 2, 3, 4, 7, 10, 11, 12, 14, 17, 20, 21, 22, 23, 24, 27, 40, etc. As every power of 10 with an exponent greater of 5 contains the suffix -illion the list of iban numbers is finite. There are exactly 30275 and the largest one is 777777.
Oban numbers

Oban numbers are defined as numbers who don't contain the letter 'o' when spelled in English. This definition is not definitive as some large numbers don't follow the guidelines for naming of numbers.

The first oban numbers are: 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 23, 25, 26, ...

Because every number name for a power of 10 greater than 3 contains the suffix thousand or -illion, the list of oban numbers is finite. There are exactly 454 and the largest one is 999.
Uban numbers

Uban numbers are defined as numbers who don't contain the letter 'u' when spelled in English. This definition is not definitive as some large numbers don't follow the guidelines for naming of numbers.

The first 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, ...
External links

Weisstein, Eric W., "Aban Number" from MathWorld.
Weisstein, Eric W., "Eban number" from MathWorld.
Weisstein, Eric W., "Iban number" from MathWorld.
Weisstein, Eric W., "Oban Number" from MathWorld.
Weisstein, Eric W., "Uban number" from MathWorld.

Mathematics Encyclopedia

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