In recreational mathematics, 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 numbers do not follow the standards of number names (such as googol and googolplex).
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, ... (sequence A006933 in the OEIS). The sequence was coined in 1990 by Neil Sloane. 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, ... (sequence A089589 in the OEIS). Since all -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, ... (sequence A008537 in the OEIS). 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, ... (sequence A008521 in the OEIS). 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, ... (sequence A008539 in the OEIS).
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, ... (sequence A008523 in the OEIS).
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, ... (sequence A089590 in the OEIS).
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, ... (sequence A008554 in the OEIS).
mathematics, a bannumber is a number that does not contain a particular letter when spelled out in English; in other words, the letter is "banned." Ban numbers...
from Foreign Adversary Controlled Applications Act, which is an effective ban or forced sale of TikTok from its parent company ByteDance. The video-sharing...
a statewide smoking ban for restaurants. Throughout the early to mid-2000s, especially between 2004 and 2007, an increasing number of states enacted a...
symbols have been banned, in part or in whole, by a number of the world's countries. As part of a broader process of decommunization, these bans have mostly...
disease, cancer, and chronic obstructive pulmonary disease. The number of smoking bans around the world increased substantially in the late 20th century...
Dancing bans are legal or religious prohibitions against dancing, which have been applied at various times in various jurisdictions around the world. This...
Firearms Use Protection Act, popularly known as the Federal Assault Weapons Ban (AWB or FAWB), was a subsection of the Violent Crime Control and Law Enforcement...
games that have been censored or banned by governments of various states in the world. Governments that have banned video games have been criticized for...
to biodiversity that they cause. A growing number of countries have instituted plastic bag bans, and a ban on single-use plastic (such as throw-away forks...
wrote a number of fu, a major literary form, part prose and part poetry, which is particularly associated with the Han era. A number of Ban's fu were...
The French ban on face covering is the result of an act of parliament passed in 2010 banning the wearing of face-covering headgear, including masks, helmets...
"Muslim ban" by Donald Trump and his supporters and critics alike, and commonly known as such, or commonly referred to as the Trump travel ban, or Trump...
The Partial Test Ban Treaty (PTBT), formally known as the 1963 Treaty Banning Nuclear Weapon Tests in the Atmosphere, in Outer Space and Under Water, prohibited...
shaving or substance abuse, players can be permanently banned from playing, although players banned for substance abuse are permitted to be reinstated two...
United Kingdom it may be the first country to ban sales of cigarettes to people born after 2008. A smoking ban in England, making it illegal to smoke in all...
In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci...
such as biographies and dictionaries. Since there have been a large number of banned books, some publishers have sought out to publish these books. The...
held the number one position for a year. To date, Simple Abundance has sold over 5 million copies and has been translated into 28 languages. Ban Breathnach's...
For nearly the entire history of film production, certain films have been banned by film censorship or review organizations for political or moral reasons...
Lu Ban (c. 507–444 BC) was a Chinese architect or master carpenter, structural engineer, and inventor, during the Zhou Dynasty. He is revered as the Chinese...
firms. The original Bausch & Lomb design is now commercially marketed as Ray-Ban Aviators, although other manufacturers also produce aviator-style sunglasses...
Ban of Benoic /ˈbæn/ (Old French: Ban de Bénoïc) is a character in Arthurian legend. King Ban first appeared by this name in the Lancelot propre part...
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