In
recreational mathematics
Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited ...
, a ban number is a number that does not contain a particular letter when spelled out in English; in other words, the letter is "banned." Ban numbers are not precisely defined, since some
large number
Large numbers are numbers significantly larger than those typically used in everyday life (for instance in simple counting or in monetary transactions), appearing frequently in fields such as mathematics, cosmology, cryptography, and statistical m ...
s do not follow the standards of number names (such as
googol
A googol is the large number 10100. In decimal notation, it is written as the digit 1 followed by one hundred zeroes: 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, ...
and
googolplex
A googolplex is the number 10, or equivalently, 10 or 1010,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 . Written out in ordinary decimal notation, it is 1 fol ...
).
There are several published sequences of ban numbers:
* The aban numbers do not contain the letter
A. The first few aban numbers are 1 through 999, 1,000,000 through 1,000,999, 2,000,000 through 2,000,999, ... The word "and" is not counted.
* The eban numbers do not contain the letter
E. The first few 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, ... . The sequence was coined in 1990 by
Neil Sloane
__NOTOC__
Neil James Alexander Sloane (born October 10, 1939) is a British-American mathematician. His major contributions are in the fields of combinatorics, error-correcting codes, and sphere packing. Sloane is best known for being the creator ...
. Coincidentally, all the numbers in the sequence are even.
* The iban numbers do not contain the letter
I. The first few iban numbers are 1, 2, 3, 4, 7, 10, 11, 12, 14, 17, 20, 21, 22, 23, 24, 27, 40, ... . Since all -illion numbers contain the letter I, there are exactly 30,275 iban numbers, the largest being 777,777.
* The oban numbers do not contain the letter
O. The first few oban numbers are 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 23, 25, 26, ... . Since "thousand" and all the -illion numbers contain the letter O, there are exactly 454 oban numbers, the largest being 999.
* The tban numbers do not contain the letter
T. The first few tban numbers are 1, 4, 5, 6, 7, 9, 11, 100, 101, 104, 105, 106, 107, 109, 111, 400, 401, 404, 405, 406, ... .
* The uban numbers do not contain the letter
U. 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, ... .
Basic properties
Aban numbers
* For 1
9, aban numbers are numbers which the integer part of N/1000 is divisible by 1000.
Eban numbers
* Eban numbers are even, due to "one", "three", "five", "seven", "nine", "eleven" and the suffix -teen all containing 'e's.
Further reading
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External links
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{{Classes of natural numbers
Integer sequences