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, far beyond those encountered in everyday life—such as simple counting or financial transactions—play a crucial role in various domains. These expansive quantities appear prominently in mathematics, cosmology, cryptography, and s ...
s do not follow the standards of number names (such as
googol
A googol is the large number 10100 or ten to the power of one hundred. In decimal notation, it is written as the digit 1 followed by one hundred zeros: 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, ...
and
googolplex
A googolplex is the large number 10, or equivalently, 10 or . Written out in ordinary decimal notation, it is 1 followed by 10100 zeroes; that is, a 1 followed by a googol of zeroes. Its prime factorization is 2 ×5.
History
In 1920, ...
).
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 dban numbers do not contain the letter
D. The first few dban numbers are 1 through 99, 1,000,000 through 1,000,099, 2,000,000 through, 2,000,099, etc...
* 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 FLSW (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 cre ...
. 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 the -illion numbers contain the letter I, there are exactly 30,275 iban numbers, the largest being 777,777.
* The nban numbers do not contain the letter
N. The first few nban numbers are 2, 3, 4, 5, 6, 8, 12, 30, 32, 33, 34, 35, 36, 38, 40, 42, 43, 44, 45, 46, 48, ... . Since "hundred", "thousand", and all the -illion numbers contain the letter N, there are exactly 42 nban numbers, the largest being 88.
* 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. Saying the word "o" for numbers with 0 in the tens place is not counted.
* The sban numbers do not contain the letter
S. The first few sban numbers are 1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23, 24, ... .
* 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, ... .
* The yban numbers do not contain the letter
Y. The first few yban numbers are 1 through 19, 100 through 119, 200 through 219, 300 through 319, ... .
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 never odd, due to "one", "three", "five", "seven", "nine", "eleven" and the suffix -teen all containing 'e's.
Further reading
*
External links
*
*
*
*
*
{{Classes of natural numbers
Integer sequences