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A006933 `Eban' numbers (the letter `e' is banned!).
(Formerly M1030)
13
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, 4000, 4002, 4004, 4006, 4030, 4032, 4034, 4036, 4040, 4042, 4044, 4046, 4050, 4052, 4054, 4056, 4060, 4062, 4064, 4066, 6000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Invented by N. J. A. Sloane circa 1990.

Theorem (N. J. A. Sloane): In English every odd number contains an `e'.

The first number that would appear in the British Eban list but not the American list is 2*10^21. - Douglas Boffey, Jun 21 2012

A085513(a(n)) = 0. - Reinhard Zumkeller, Jan 23 2015

REFERENCES

J. C. Hernandez et al., "Characterization of Eban numbers", pp. 197-200, Journal of Recreational Mathematics, 31 (3) 2002-2003.

Georges Perec, La disparition, Editions Gallimard, Paris, 1969; English translation: A Void, Harvill, 1994. (A novel that does does not use the letter "e".)

Georges Perec, Les Revenentes [a novel in which the only vowel that appears is `e']. - From Simon Plouffe, Mar 12 2010

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Author?, What comes next? in Science News for Kids.

Roel and Bas van Dijk, Numerals package, Hackage (Haskell packages)

Eric Weisstein's World of Mathematics, Eban Number

Index entries for sequences related to number of letters in n

EXAMPLE

2052 is in the sequence because written out in English words, "two thousand fifty-two," it does not contain a single instance of the letter E.

2053 (two thousand fifty-three) is not in the sequence because written out it contains two instances of E.

PROG

(MAGMA) [ n : n in [1..100] | forall{ i : i in [1..#seq] | seq[i] in eban[(i-1)mod 3+1]} where seq is Intseq(n) ] where eban is [[0, 2, 4, 6], [0, 3, 4, 5, 6], [0]]; - from Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006

(Haskell)

import Data.Maybe (fromJust)

import Data.Text (Text); import qualified Data.Text as T (unpack)

import Text.Numeral.Grammar.Reified (defaultInflection)

import qualified Text.Numeral.Language.EN as EN  -- see link

a006933 n = a006933_list !! (n-1)

a006933_list = filter (T.all (/= 'e') . numeral) [0..] where

   numeral :: Integer -> Text

   numeral = fromJust . EN.gb_cardinal defaultInflection

-- Reinhard Zumkeller, Jan 23 2015

CROSSREFS

Cf. A082504.

Cf. A085513, A008520 (complement), A089589 (ban i), A008521 (ban o), A008523 (ban t), A089590 (ban u).

Sequence in context: A106274 A204661 A077633 * A046847 A121069 A100838

Adjacent sequences:  A006930 A006931 A006932 * A006934 A006935 A006936

KEYWORD

word,nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from WG Zeist, Aug 28 2012

STATUS

approved

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Last modified July 30 06:01 EDT 2015. Contains 260124 sequences.