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A006933
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'Eban' numbers (the letter 'e' is banned!).
(Formerly M1030)
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24
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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)
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OFFSET
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1,1
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COMMENTS
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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
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REFERENCES
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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).
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LINKS
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EXAMPLE
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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.
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PROG
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(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
(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
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CROSSREFS
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KEYWORD
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word,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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