Ban number

Ban numbers are numbers that exclude a specific letter when spelled out.

There are several published sequences of ban numbers:

• The aban numbers exclude 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 exclude 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.
• The eban numbers exclude 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 [{{fullurl:OEIS:{{{id}}}}} {{{id}}}] in OEIS). The sequence was coined in 1990 by Neil Sloane. Coincidentally, all the numbers in the sequence are even.
• The iban numbers exclude 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 [{{fullurl:OEIS:{{{id}}}}} {{{id}}}] in OEIS). Since all the -illion numbers contain the letter I, there are exactly 30,275 iban numbers, the largest being 777,777.
• The nban numbers exclude 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 [{{fullurl:OEIS:{{{id}}}}} {{{id}}}] in 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 exclude 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 [{{fullurl:OEIS:{{{id}}}}} {{{id}}}] in 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 exclude 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 [{{fullurl:OEIS:{{{id}}}}} {{{id}}}] in OEIS).
• The tban numbers exclude 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 [{{fullurl:OEIS:{{{id}}}}} {{{id}}}] in OEIS).
• The uban numbers exclude 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 [{{fullurl:OEIS:{{{id}}}}} {{{id}}}] in OEIS).
• The yban numbers exclude the letter Y. The first few yban numbers are 1 through 19, 100 through 119, 200 through 219, 300 through 319, ... (sequence [{{fullurl:OEIS:{{{id}}}}} {{{id}}}] in OEIS).

Basic properties

All odd numbers always contain the letter "e", such as "one", "three", "five", "seven", "nine", "eleven", and all the -teen numbers (13-19).