A006933 'Eban' numbers (the letter 'e' is banned!). (Formerly M1030)

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

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 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

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

Brady Haran and N. J. A. Sloane, What Number Comes Next? (2018), Numberphile video

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]]; // 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
(Python)
from num2words import num2words
[n for n in range(6001) if 'e' not in num2words(n)] # Indranil Ghosh, Jul 05 2017
(PARI) is(n)=!setsearch(Set(Vec(English(n))), "e") \\ See A052360 for English(). - M. F. Hasler, Apr 01 2019

Crossrefs

Cf. A082504.

Cf. A085513, A008520 (complement), A008521 (ban o), A008523 (ban t), A089589 (ban i), A089590 (ban u), A014254 (a French version), A287876 (a Hebrew version).

Cf. A008537 (without 'n'), A072956 (turban numbers: without r, t or u), A072957 (urban numbers: without r or u), A089589 (without 'i').

Sequence in context: A284919 A279419 A077633 * A046847 A339759 A121069

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

More cross-references from M. F. Hasler, Apr 01 2019

Status

approved