A006933 -id:A006933 - cp's OEIS frontend

A008520 Numbers whose American English name contains the letter 'e'.

0, 1, 3, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 33, 35, 37, 38, 39, 41, 43, 45, 47, 48, 49, 51, 53, 55, 57, 58, 59, 61, 63, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90

Offset: 1

N. J. A. Sloane

A085513(a(n)) > 0. - Reinhard Zumkeller, Jan 23 2015

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Roel and Bas van Dijk, Numerals package, Hackage (Haskell packages)
Index entries for sequences related to number of letters in n

Cf. A006933 (complement), A085513.

Cf. A008519 (o), A008522 (t), A008536 (n), A008538 (s), A008540 (f), A008553 (y).

import Data.Maybe (fromJust)
import Data.Text (Text); import qualified Data.Text as T (any)
import Text.Numeral.Grammar.Reified (defaultInflection)
import qualified Text.Numeral.Language.EN as EN  -- see link
a008520 n = a008520_list !! (n-1)
a008520_list = filter (T.any (== 'e') . numeral) [0..] where
   numeral :: Integer -> Text
   numeral = fromJust . EN.gb_cardinal defaultInflection
-- Reinhard Zumkeller, Jan 23 2015

A008520Q[n_]:=StringContainsQ[IntegerName[n,"Words"],"e"];Select[Range[0,200],A008520Q] (* Paolo Xausa, Aug 11 2023 *)

Name edited by Michael De Vlieger, Aug 11 2023

A089589 Iban numbers (the letter i is banned from the English name of the number).

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 10, 11, 12, 14, 17, 20, 21, 22, 23, 24, 27, 40, 41, 42, 43, 44, 47, 70, 71, 72, 73, 74, 77, 100, 101, 102, 103, 104, 107, 110, 111, 112, 114, 117, 120, 121, 122, 123, 124, 127, 140, 141, 142, 143, 144, 147, 170, 171, 172, 173, 174, 177, 200, 201

Offset: 1

Eric W. Weisstein, Nov 09 2003

Blind numbers. - Cino Hilliard, May 03 2004

There are 30276 terms, ending in 777777. - Michael S. Branicky, Aug 04 2022

Michael S. Branicky, Table of n, a(n) for n = 1..30276 (full sequence; terms 1..10000 from Reinhard Zumkeller)
Roel and Bas van Dijk, Numerals package, Hackage (Haskell packages).
Eric Weisstein's World of Mathematics, Iban Number
Wikipedia, Names of Large Numbers
Index entries for sequences related to number of letters in n

Cf. A006933 (ban e), A008521 (ban o), A008523 (ban t), A089590 (ban u).

import Data.Maybe (fromJust)
import Data.Text (Text); import qualified Data.Text as T (all)
import Text.Numeral.Grammar.Reified (defaultInflection)
import qualified Text.Numeral.Language.EN as EN  -- see link
a089589 n = a089589_list !! (n-1)
a089589_list = filter (T.all (/= 'i') . numeral) [0..] where
   numeral :: Integer -> Text
   numeral = fromJust . EN.gb_cardinal defaultInflection
-- Reinhard Zumkeller, Jan 23 2015

from itertools import islice
from num2words import num2words
def agen(): yield from (k for k in range(10**6) if "i" not in num2words(k))
print(list(islice(agen(), 60))) # Michael S. Branicky, Aug 04 2022

A089590 Uban numbers (the letter u is banned from the English name of the number).

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 90, 91, 92, 93, 95, 96, 97, 98, 99

Offset: 1

Eric W. Weisstein, Nov 09 2003

The sequence of uban numbers first differs from A052406 (the numbers not containing the digit 4) at the term 40 (forty), which is a uban number but is not 4-less.

Daniel Arribas and Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 (first 89 terms from Daniel Arribas)
Roel and Bas van Dijk, Numerals package, Hackage (Haskell packages)
Eric Weisstein's World of Mathematics, Uban Number
Index entries for sequences related to number of letters in n

Cf. A052406.

Cf. A006933 (ban e), A089589 (ban i), A008521 (ban o), A008523 (ban t).

import Data.Maybe (fromJust)
import Data.Text (Text); import qualified Data.Text as T (all)
import Text.Numeral.Grammar.Reified (defaultInflection)
import qualified Text.Numeral.Language.EN as EN  -- see link
a089590 n = a089590_list !! (n-1)
a089590_list = filter (T.all (/= 'u') . numeral) [0..] where
   numeral :: Integer -> Text
   numeral = fromJust . EN.gb_cardinal defaultInflection
-- Reinhard Zumkeller, Jan 23 2015

from num2words import num2words
from itertools import islice, product
def ok(n): return "u" not in num2words(n)
def agen(): # generator of terms < 10**304
    base, pows = [k for k in range(1, 1000) if ok(k)], [1]
    yield from ([0] if ok(0) else []) + base
    for e in range(3, 304, 3):
        if "u" not in num2words(10**e)[4:]:
            pows = [10**e] + pows
            for t in product([0] + base, repeat=len(pows)):
                if t[0] == 0: continue
                yield sum(t[i]*pows[i] for i in range(len(t)))
print(list(islice(agen(), 100))) # Michael S. Branicky, Aug 19 2022

a(1) = 0 prepended by Reinhard Zumkeller, Jan 23 2015

A008521 Numbers that do not contain the letter 'o'.

Original entry on oeis.org

3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 23, 25, 26, 27, 28, 29, 30, 33, 35, 36, 37, 38, 39, 50, 53, 55, 56, 57, 58, 59, 60, 63, 65, 66, 67, 68, 69, 70, 73, 75, 76, 77, 78, 79, 80, 83, 85, 86, 87, 88, 89, 90, 93, 95, 96, 97, 98, 99, 300, 303, 305, 306, 307

Offset: 1

N. J. A. Sloane

There are exactly 454 oban numbers. - Eric W. Weisstein, Nov 09 2003

Reinhard Zumkeller, Table of n, a(n) for n = 1..454
Roel and Bas van Dijk, Numerals package, Hackage (Haskell packages).
Eric Weisstein's World of Mathematics, Oban Number
Index entries for sequences related to number of letters in n

Cf. A006933 (ban e), A089589 (ban i), A008523 (ban t), A089590 (ban u).

import Data.Maybe (fromJust)
import Data.Text (Text); import qualified Data.Text as T (all)
import Text.Numeral.Grammar.Reified (defaultInflection)
import qualified Text.Numeral.Language.EN as EN  -- see link
a008521 n = a008521_list !! (n-1)
a008521_list = filter (T.all (/= 'o') . numeral) [0..] where
   numeral :: Integer -> Text
   numeral = fromJust . EN.gb_cardinal defaultInflection
-- Reinhard Zumkeller, Jan 23 2015

from num2words import num2words
afull = [k for k in range(1000) if "o" not in num2words(k)]
print(afull[:70]) # Michael S. Branicky, Aug 18 2022

A008523 Numbers that do not contain the letter 't'.

Original entry on oeis.org

0, 1, 4, 5, 6, 7, 9, 11, 100, 101, 104, 105, 106, 107, 109, 111, 400, 401, 404, 405, 406, 407, 409, 411, 500, 501, 504, 505, 506, 507, 509, 511, 600, 601, 604, 605, 606, 607, 609, 611, 700, 701, 704, 705, 706, 707, 709, 711, 900, 901, 904, 905, 906, 907, 909, 911, 1000000, 1000001, 1000004, 1000005

Offset: 1

N. J. A. Sloane

See also A006933, the eban numbers (numbers not containing 'e'), and A089589 (the iban numbers). This sequence might correspondingly be called the "tban" numbers. - WG Zeist, Aug 31 2012

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Roel and Bas van Dijk, Numerals package, Hackage (Haskell packages)
Index entries for sequences related to number of letters in n

Cf. A006933 (ban e), A089589 (ban i), A008521 (ban o), A089590 (ban u).

Complement of A008522.

-- import Data.Maybe (fromJust)
import Data.Text (Text); import qualified Data.Text as T (all)
import Text.Numeral.Grammar.Reified (defaultInflection)
import qualified Text.Numeral.Language.EN as EN  -- see link
a008523 n = a008523_list !! (n-1)
a008523_list = filter (T.all (/= 't') . numeral) [0..] where
   numeral :: Integer -> Text
   numeral = fromJust . EN.gb_cardinal defaultInflection
-- Reinhard Zumkeller, Jan 23 2015

from num2words import num2words
from itertools import islice, product
def ok(n): return "t" not in num2words(n)
def agen(): # generator of terms < 10**304
    base, pows = [k for k in range(1, 1000) if ok(k)], [1]
    yield from ([0] if ok(0) else []) + base
    for e in range(3, 304, 3):
        if "u" not in num2words(10**e)[4:]:
            pows = [10**e] + pows
            for t in product([0] + base, repeat=len(pows)):
                if t[0] == 0: continue
                yield sum(t[i]*pows[i] for i in range(len(t)))
print(list(islice(agen(), 60))) # Michael S. Branicky, Aug 19 2022

a(57)-a(60) from WG Zeist, Aug 31 2012

A014254 Liponombres: numbers whose French name does not contain the letter "e".

Original entry on oeis.org

1, 3, 5, 6, 8, 10, 18, 20, 23, 25, 26, 28, 1000000, 1000001, 1000003, 1000005, 1000006, 1000008, 1000010, 1000018, 1000020, 1000023, 1000025, 1000026, 1000028, 3000000, 3000001, 3000003, 3000005, 3000006, 3000008, 3000010

Offset: 1

Olivier Gérard

In French also called: les nombres "évites" ou "apparés".
Could also be called les nombres "epers". - Benoit Cloitre, May 05 2003
French version of eban numbers (A006933): no "e" in name of number in French - "e" perd ("e" lost)!

			a(1) = 1 ("un"), a(2) = 3 ("trois", not "dEux")

Georges Perec, La disparition, Editions Gallimard, Paris, 1969; English translation: A Void, Harvill, 1994. (A novel that does not use the letter "e". These numbers are not mentioned, however.)

N. Graner, Liponombres [<>]

Cf. A006933, A050280 (primes); A167507, A139212, A007005, A139121, A233185.

is_A014254(n)=!setsearch(Set(Vec(French(n))),"e") \\ See A167507 for French(). - M. F. Hasler, Nov 11 2015

Additional comments from Bruno Salvy (Bruno.Salvy(AT)inria.fr) and Nicolas Graner (Nicolas.Graner(AT)cri.u-psud.fr), May 11 2003
Corrected by Don Reble, Nov 19 2006
Edited by M. F. Hasler, Nov 11 2015

A054047 Numbers which can be read as (possibly different) numbers when rotated by 180 degrees (final zeros allowed).

Original entry on oeis.org

0, 1, 6, 8, 9, 10, 11, 16, 18, 19, 60, 61, 66, 68, 69, 80, 81, 86, 88, 89, 90, 91, 96, 98, 99, 100, 101, 106, 108, 109, 110, 111, 116, 118, 119, 160, 161, 166, 168, 169, 180, 181, 186, 188, 189, 190, 191, 196, 198, 199, 600, 601, 606, 608, 609, 610, 611, 616, 618

Offset: 0

Alain Zalmanski (alain.zalmanski(AT)cybercable.fr), Apr 28 2000

A. Zalmanski, Some fun with figures and letters, unpublished.

Cf. A006933, A014254, A045574.

Corrected and extended by James Sellers, Apr 30 2000

A072956 Turban numbers: without letters r, t, or u.

Original entry on oeis.org

1, 5, 6, 7, 9, 11, 1000000, 1000001, 1000005, 1000006, 1000007, 1000009, 1000011, 5000000, 5000001, 5000005, 5000006, 5000007, 5000009, 5000011, 6000000, 6000001, 6000005, 6000006, 6000007, 6000009, 6000011, 7000000, 7000001, 7000005, 7000006, 7000007, 7000009

Offset: 1

Michael Joseph Halm, Aug 13 2002

M. J. Halm, Sequences (Re)discovered, Mpossibilities 81 (Aug. 2002).

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A006933 (eban numbers: without 'e'), A008521 (without 'o'), A008523 (without 't'), A008537 (without 'n'), A089590 (without 'u'), A072957 (urban numbers: without r or u), A089589 (without 'i').

is(n)=!setintersect(Set(Vec(English(n))),["r","t","u"]) \\ See A052360 for English(). - M. F. Hasler, Apr 01 2019

from num2words import num2words
from itertools import islice, product
def ok(n): return set(num2words(n)) & {"r", "t", "u"} == set()
def agen(): # generator of terms < 10**304
    base, pows = [k for k in range(1, 1000) if ok(k)], [1]
    yield from ([0] if ok(0) else []) + base
    for e in range(3, 304, 3):
        if set(num2words(10**e)[4:]) & {"r", "t", "u"} == set():
            pows = [10**e] + pows
            for t in product([0] + base, repeat=len(pows)):
                if t[0] == 0: continue
                yield sum(t[i]*pows[i] for i in range(len(t)))
print(list(islice(agen(), 66))) # Michael S. Branicky, Aug 19 2022

A072957 Urban numbers: without 'r' or 'u'.

Original entry on oeis.org

1, 2, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 25, 26, 27, 28, 29, 50, 51, 52, 55, 56, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 72, 75, 76, 77, 78, 79, 80, 81, 82, 85, 86, 87, 88, 89, 90, 91, 92, 95, 96, 97, 98, 99, 1000000, 1000001, 1000002

Offset: 1

Michael Joseph Halm, Aug 13 2002

M. J. Halm, Sequences (Re)discovered, Mpossibilities 81 (Aug. 2002).

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A006933 (eban numbers: without 'e'), A008521 (without 'o'), A008523 (without 't'), A008537 (without 'n'), A089590 (without 'u'), A072956 (turban numbers: without r, t or u), A089589 (without 'i').

is(n)=!setintersect(Set(Vec(English(n))),["r","u"]) \\ See A052360 for English(). - M. F. Hasler, Apr 01 2019
/* Alternate code, not using English(): (valid for 1 <= n < one trillion, which should be forbidden due to the 'r' but returns 1) */
is(n)={setintersect( Set(digits(n)), [3,4]) && return; !while(n=divrem(n,10^6), n[2]<100||return; n=n[1])} \\ M. F. Hasler, Apr 01 2019

from num2words import num2words
from itertools import islice, product
def ok(n): return set(num2words(n)) & {"r", "u"} == set()
def agen(): # generator of terms < 10**304
    base, pows = [k for k in range(1, 1000) if ok(k)], [1]
    yield from ([0] if ok(0) else []) + base
    for e in range(3, 304, 3):
        if set(num2words(10**e)[4:]) & {"r", "u"} == set():
            pows = [10**e] + pows
            for t in product([0] + base, repeat=len(pows)):
                if t[0] == 0: continue
                yield sum(t[i]*pows[i] for i in range(len(t)))
print(list(islice(agen(), 66))) # Michael S. Branicky, Aug 19 2022

Missing term 52 inserted by Michael S. Branicky, Aug 19 2022

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

cp's OEIS Frontend

A008520 Numbers whose American English name contains the letter 'e'.

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A089589 Iban numbers (the letter i is banned from the English name of the number).

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A089590 Uban numbers (the letter u is banned from the English name of the number).

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A008521 Numbers that do not contain the letter 'o'.

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A008523 Numbers that do not contain the letter 't'.

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A014254 Liponombres: numbers whose French name does not contain the letter "e".

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PARI

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A054047 Numbers which can be read as (possibly different) numbers when rotated by 180 degrees (final zeros allowed).

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A072956 Turban numbers: without letters r, t, or u.

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