

A006933


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


20



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
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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. 197200, Journal of Recreational Mathematics, 31 (3) 20022003.
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
Roel and Bas van Dijk, Numerals package, Hackage (Haskell packages)
Brady Haran and Neil 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 fiftytwo", it does not contain a single instance of the letter E.
2053 (two thousand fiftythree) 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[(i1)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)sergeihaller.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 !! (n1)
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
print [n for n in xrange(6001) if num2words(n).count('e')==0] # 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 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
More crossreferences from M. F. Hasler, Apr 01 2019


STATUS

approved



