Inrecreational mathematics, aban 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 somelarge numbers do not follow the standards of number names (such asgoogol andgoogolplex).

There are several published sequences of ban numbers:

• Theaban numbers do not contain the letterA. 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.
• Thedban numbers do not contain the letterD. The first few dban numbers are 1 through 99, 1,000,000 through 1,000,099, 2,000,000 through, 2,000,099, etc...
• Theeban numbers do not contain the letterE. 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, 2006, 2030, 2032, 2034, 2036, 2040, 2042, 2044, 2046, 2050, 2052, 2054, 2056, 2060, 2062, 2064, 2066... (sequenceA006933 in theOEIS). The sequence was coined in 1990 byNeil Sloane. Coincidentally, all the numbers in the sequence are even.
• Theiban numbers do not contain the letterI. The first few iban numbers are 1, 2, 3, 4, 7, 10, 11, 12, 14, 17, 20, 21, 22, 23, 24, 27, 40, ... (sequenceA089589 in theOEIS). Since all the -illion numbers contain the letter I, there are exactly 30,275 iban numbers, the largest being 777,777.
• Thenban numbers do not contain the letterN. The first few nban numbers are 0, 2, 3, 4, 5, 6, 8, 12, 30, 32, 33, 34, 35, 36, 38, 40, 42, 43, 44, 45, 46, 48, ... (sequenceA008537 in theOEIS). Since "hundred", "thousand", and all the -illion numbers contain the letter N, there are exactly 43 nban numbers, the largest being 88.
• Theoban numbers do not contain the letterO. 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, ... (sequenceA008521 in theOEIS). 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.
• Thesban numbers do not contain the letterS. 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, ... (sequenceA008539 in theOEIS).
• Thetban numbers do not contain the letterT. 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, ... (sequenceA008523 in theOEIS).
• Theuban numbers do not contain the letterU. 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, ... (sequenceA089590 in theOEIS).
• Theyban numbers do not contain the letterY. The first few yban numbers are 1 through 19, 100 through 119, 200 through 219, 300 through 319, ... (sequenceA008554 in theOEIS).

• For 1<N<10⁹, aban numbers are numbers which the integer part of N/1000 is divisible by 1000.

• Eban numbers are never odd, due to "one", "three", "five", "seven", "nine", "eleven" and the suffix -teen all containing 'e's.

• Hernandez, J. C.; Mex-Perera, C.; Shepherd, S. J. (2002–2003).Characterization of Eban Numbers (31 ed.). J. Recr. Math. pp. 197–200.

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

• Integer sequences

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