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

%I A006933 M1030 #73 Feb 16 2025 08:32:31
%S A006933 2,4,6,30,32,34,36,40,42,44,46,50,52,54,56,60,62,64,66,2000,2002,2004,
%T A006933 2006,2030,2032,2034,2036,2040,2042,2044,2046,2050,2052,2054,2056,
%U A006933 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
%N A006933 'Eban' numbers (the letter 'e' is banned!).
%C A006933 Invented by _N. J. A. Sloane_ circa 1990.
%C A006933 Theorem (_N. J. A. Sloane_): in English every odd number contains an 'e'.
%C A006933 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
%C A006933 A085513(a(n)) = 0. - _Reinhard Zumkeller_, Jan 23 2015
%D A006933 J. C. Hernandez et al., "Characterization of Eban numbers", pp. 197-200, Journal of Recreational Mathematics, 31 (3) 2002-2003.
%D A006933 Georges Perec, La disparition, Editions Gallimard, Paris, 1969; English translation: A Void, Harvill, 1994. (A novel that does not use the letter "e".)
%D A006933 Georges Perec, Les Revenentes [a novel in which the only vowel that appears is 'e']. - From _Simon Plouffe_, Mar 12 2010
%D A006933 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006933 Reinhard Zumkeller, <a href="/A006933/b006933.txt">Table of n, a(n) for n = 1..10000</a>
%H A006933 Roel and Bas van Dijk, <a href="http://hackage.haskell.org/package/numerals">Numerals package</a>, Hackage (Haskell packages)
%H A006933 Brady Haran and N. J. A. Sloane, <a href="https://www.youtube.com/watch?v=OeGSQggDkxI">What Number Comes Next?</a> (2018), Numberphile video
%H A006933 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EbanNumber.html">Eban Number</a>
%H A006933 <a href="/index/Lc#letters">Index entries for sequences related to number of letters in n</a>
%e A006933 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.
%e A006933 2053 (two thousand fifty-three) is not in the sequence because written out it contains two instances of E.
%o A006933 (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
%o A006933 (Haskell)
%o A006933 import Data.Maybe (fromJust)
%o A006933 import Data.Text (Text); import qualified Data.Text as T (unpack)
%o A006933 import Text.Numeral.Grammar.Reified (defaultInflection)
%o A006933 import qualified Text.Numeral.Language.EN as EN  -- see link
%o A006933 a006933 n = a006933_list !! (n-1)
%o A006933 a006933_list = filter (T.all (/= 'e') . numeral) [0..] where
%o A006933    numeral :: Integer -> Text
%o A006933    numeral = fromJust . EN.gb_cardinal defaultInflection
%o A006933 -- _Reinhard Zumkeller_, Jan 23 2015
%o A006933 (Python)
%o A006933 from num2words import num2words
%o A006933 [n for n in range(6001) if 'e' not in num2words(n)] # _Indranil Ghosh_, Jul 05 2017
%o A006933 (PARI) is(n)=!setsearch(Set(Vec(English(n))), "e") \\ See A052360 for English(). - _M. F. Hasler_, Apr 01 2019
%Y A006933 Cf. A082504.
%Y A006933 Cf. A085513, A008520 (complement), A008521 (ban o), A008523 (ban t), A089589 (ban i), A089590 (ban u), A014254 (a French version), A287876 (a Hebrew version).
%Y A006933 Cf. A008537 (without 'n'), A072956 (turban numbers: without r, t or u), A072957 (urban numbers: without r or u), A089589 (without 'i').
%K A006933 word,nonn
%O A006933 1,1
%A A006933 _N. J. A. Sloane_
%E A006933 More terms from _WG Zeist_, Aug 28 2012
%E A006933 More cross-references from _M. F. Hasler_, Apr 01 2019