A008520 -id:A008520 - cp's OEIS frontend

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

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

N. J. A. Sloane

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

			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.

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).

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

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').

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

[ 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

is(n)=!setsearch(Set(Vec(English(n))), "e") \\ See A052360 for English(). - M. F. Hasler, Apr 01 2019

from num2words import num2words
[n for n in range(6001) if 'e' not in num2words(n)] # Indranil Ghosh, Jul 05 2017

More terms from WG Zeist, Aug 28 2012

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

A008522 Numbers whose American English name contains the letter 't'.

Original entry on oeis.org

2, 3, 8, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77

Offset: 1

N. J. A. Sloane

			8 = eigh{t}.

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A008519 (o), A008520 (e), A008536 (n), A008538 (s), A008540 (f), A008553 (y).

A008522Q[n_]:=StringContainsQ[IntegerName[n,"Words"],"t"];Select[Range[0,200],A008522Q] (* Paolo Xausa, Aug 12 2023 *)

Name edited by Paolo Xausa, Aug 12 2023

A008536 Numbers whose American English name contains the letter 'n'.

Original entry on oeis.org

1, 7, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 37, 39, 41, 47, 49, 51, 57, 59, 61, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 87, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107

Offset: 1

N. J. A. Sloane

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A008519 (o), A008520 (e), A008522 (t), A008538 (s), A008540 (f), A008553 (y).

A008536Q[n_]:=StringContainsQ[IntegerName[n,"Words"],"n"];Select[Range[0,200],A008536Q] (* Paolo Xausa, Aug 12 2023 *)

Name edited by Paolo Xausa, Aug 12 2023

A008519 Numbers whose American English name contains the letter 'o'.

Original entry on oeis.org

0, 1, 2, 4, 14, 21, 22, 24, 31, 32, 34, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 54, 61, 62, 64, 71, 72, 74, 81, 82, 84, 91, 92, 94, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123

Offset: 1

N. J. A. Sloane

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A008520 (e), A008522 (t), A008536 (n), A008538 (s), A008540 (f), A008553 (y).

A008519Q[n_]:=StringContainsQ[IntegerName[n,"Words"],"o"];Select[Range[0,200],A008519Q] (* Paolo Xausa, Aug 10 2023 *)

Name edited by Paolo Xausa, Aug 12 2023

A008538 Numbers whose American English name contains the letter 's'.

Original entry on oeis.org

6, 7, 16, 17, 26, 27, 36, 37, 46, 47, 56, 57, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 86, 87, 96, 97, 106, 107, 116, 117, 126, 127, 136, 137, 146, 147, 156, 157, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173

Offset: 1

N. J. A. Sloane

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A008519 (o), A008520 (e), A008522 (t), A008536 (n), A008540 (f), A008553 (y).

A008538Q[n_]:=StringContainsQ[IntegerName[n,"Words"],"s"];Select[Range[0,200],A008538Q] (* Paolo Xausa, Aug 12 2023 *)

Name edited by Paolo Xausa, Aug 12 2023

A008540 Numbers whose American English name contains the letter 'f'.

Original entry on oeis.org

4, 5, 14, 15, 24, 25, 34, 35, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 64, 65, 74, 75, 84, 85, 94, 95, 104, 105, 114, 115, 124, 125, 134, 135, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158

Offset: 1

N. J. A. Sloane

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A008519 (o), A008520 (e), A008522 (t), A008536 (n), A008538 (s), A008553 (y).

A008540Q[n_]:=StringContainsQ[IntegerName[n,"Words"],"f"];Select[Range[0,200],A008540Q] (* Paolo Xausa, Aug 12 2023 *)

Name edited by Paolo Xausa, Aug 12 2023

A008553 Numbers whose American English name contains the letter 'y'.

Original entry on oeis.org

20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85

Offset: 1

N. J. A. Sloane

Paolo Xausa, Table of n, a(n) for n = 1..10000
Tanya Khovanova, Non Recursions

Cf. A008519 (o), A008520 (e), A008522 (t), A008536 (n), A008538 (s), A008540 (f).

A008553Q[n_]:=StringContainsQ[IntegerName[n,"Words"],"y"];Select[Range[0,200],A008553Q] (* Paolo Xausa, Aug 12 2023 *)

Name edited by Paolo Xausa, Aug 12 2023

A085513 Number of "e"s in n (in English).

Original entry on oeis.org

1, 1, 0, 2, 0, 1, 0, 2, 1, 1, 1, 3, 2, 2, 2, 2, 2, 4, 3, 3, 1, 2, 1, 3, 1, 2, 1, 3, 2, 2, 0, 1, 0, 2, 0, 1, 0, 2, 1, 1, 0, 1, 0, 2, 0, 1, 0, 2, 1, 1, 0, 1, 0, 2, 0, 1, 0, 2, 1, 1, 0, 1, 0, 2, 0, 1, 0, 2, 1, 1, 2, 3, 2, 4, 2, 3, 2, 4, 3, 3, 1, 2, 1, 3, 1, 2, 1, 3, 2, 2, 1, 2, 1, 3, 1, 2, 1, 3, 2, 2

Offset: 0

Samuel Thompson (samuelt(AT)ugcs.caltech.edu), Jul 03 2003

a(A006933(n)) = 0; a(A008520(n)) > 0. - Reinhard Zumkeller, Jan 23 2015

a(A006933(n)) = 0; a(A008520(n)) > 0; a(A121065(n)) = n and a(m) != n for m < A121065(n). - Reinhard Zumkeller, Jan 24 2015

			a(123) = 5 because "onE hundrEd twEnty-thrEE" has 5 e's.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Roel and Bas van Dijk, Numerals package, Hackage (Haskell packages)
Robert G. Wilson v, English names for the numbers from 0 to 11159 without spaces or hyphens .
Index entries for sequences related to number of letters in n

Cf. A005589.

Cf. A006933, A008520.

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
a085513 = length . filter (== 'e') . T.unpack . numeral where
   numeral :: Integer -> Text
   numeral = fromJust . EN.gb_cardinal defaultInflection
-- Reinhard Zumkeller, Jan 23 2015

StringCount[IntegerName/@Range[0,99],"e"] (* Ivan N. Ianakiev, Mar 25 2017 *)

from num2words import num2words
def A085513(n):
    return num2words(n).count('e') # Chai Wah Wu, Dec 20 2019

A121065 a(n) is the smallest number in English which contains n letter 'E's.

Original entry on oeis.org

2, 0, 3, 11, 17, 111, 117, 317, 1317, 3317, 11317, 17317, 111317, 117317, 317317, 1317317, 3317317, 11317317, 17317317, 111317317, 117317317, 317317317, 1317317317, 3317317317, 11317317317, 17317317317, 111317317317, 117317317317, 317317317317, 1317317317317

Offset: 0

Ray G. Opao, Aug 10 2006

4, 5, 6, 8, 9 never appear in any of these numbers because in each case there is a smaller digit with the same number of e's. 2 (the smallest number with no e's) never appears in any term after a(0). - Sean A. Irvine, Nov 10 2009

A085513(a(n)) = n and A085513(m) != n for m < a(n). - Reinhard Zumkeller, Jan 24 2015

			a(2) = THREE, which has two Es.

Index entries for sequences related to number of letters in n

Cf. A085513, A008520, A006933. Variant of A036448.

import Data.List (elemIndex); import Data.Maybe (fromJust)
a121065 = fromJust . (`elemIndex` a085513_list)
-- Reinhard Zumkeller, Jan 24 2015

From Chai Wah Wu, Dec 20 2019: (Start)
a(n) = a(n-1) + 1000*a(n-7) - 1000*a(n-8) for n > 9 (conjectured).
G.f.: (-1000*x^9 + 3000*x^8 - 1800*x^7 + 6*x^6 + 94*x^5 + 6*x^4 + 8*x^3 + 3*x^2 - 2*x + 2)/((x - 1)*(1000*x^7 - 1)) (conjectured). (End)

More terms Sean A. Irvine, Nov 10 2009
a(19) - a(21) added by Reinhard Zumkeller, Jan 24 2015
a(22) - a(29) from Chai Wah Wu, Dec 20 2019

A095790 Numbers whose name in English contains an "r".

Original entry on oeis.org

3, 4, 13, 14, 23, 24, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 53, 54, 63, 64, 73, 74, 83, 84, 93, 94, 103, 104, 113, 114, 123, 124, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148

Offset: 1

Michael Joseph Halm, Jul 10 2004

A008520 are numbers which contain an "e", A008540 an "f", A011538 a "g", A008536 an "n", A008519 an "o", A008538 an "s", A008522 a "t", A011534 a "u", A011532 a "w", A011536 an "x" and A008553 a "y"

			a(1) = 3 because "three" contains an "r", 0, 1 and 2 do not

Cf. A008520, A008540, A011538, A008536, A008519, A008538, A008522, A011534, A011532, A011536, A008553.

cp's OEIS Frontend

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

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A008522 Numbers whose American English name contains the letter 't'.

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A008536 Numbers whose American English name contains the letter 'n'.

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A008519 Numbers whose American English name contains the letter 'o'.

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A008538 Numbers whose American English name contains the letter 's'.

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A008540 Numbers whose American English name contains the letter 'f'.

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A008553 Numbers whose American English name contains the letter 'y'.

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A085513 Number of "e"s in n (in English).

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