A089589 -id:A089589 - 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

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

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

A008537 Numbers that do not contain the letter 'n'.

Original entry on oeis.org

0, 2, 3, 4, 5, 6, 8, 12, 30, 32, 33, 34, 35, 36, 38, 40, 42, 43, 44, 45, 46, 48, 50, 52, 53, 54, 55, 56, 58, 60, 62, 63, 64, 65, 66, 68, 80, 82, 83, 84, 85, 86, 88

Offset: 1

N. J. A. Sloane

From M. F. Hasler, Apr 01 2019: (Start)
This sequence contains 42 nonzero terms below 10^9, plus the initial a(1) = 0.
Since "hundred", "thousand", "million" etc. are forbidden, the only way to extend the sequence would be to use long scale with "milliard" for 10^9: then the next term would be a(44) = 2*10^9 = "two milliards", a(45) = 2*10^9 + 2, and so on.
The 2019 "April Fools contest" on codeforces.com referred to these numbers as "Kanban numbers", i.e., numbers which ban the letters 'k', 'a' and 'n'. But no 'k' ever appears, and unless we consider "milliard", 'a' only appears (in "thousand" and later "quadrillion") in conjunction with 'n', which therefore is the only relevant. So "n-ban (or maybe: anban) numbers" would be more a adequate name. (End)

GCHQ, The GCHQ Puzzle Book, Penguin, 2016. See Puzzle 114, p. 56.
Mariia Mykhailova (alias Nickolas), April Fools Day Contest 2019 - B: Kanban Numbers, on codeforces.com, April 1, 2019.

Cf. A006933 (eban numbers: without 'e'), A089589 (without 'i'), A008521 (without 'o'), A089590 (without 'u'), A008523 (without 't'), A072956 (turban numbers: without r, t or u), A072957 (urban numbers: without r or u).

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

from num2words import num2words
afull = [k for k in range(100) if "n" not in num2words(k)]
print(afull) # Michael S. Branicky, Aug 18 2022

Edited by M. F. Hasler, Apr 01 2019

A095763 Numbers whose name in English contains an "i".

Original entry on oeis.org

5, 6, 8, 9, 13, 15, 16, 18, 19, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99

Offset: 1

Michael Joseph Halm, Jul 10 2004

			a(5) = 13 because "thirteen" contains an "i" and is the fifth integer to do so

A001477 \ A089589. [From R. J. Mathar, Apr 28 2009]

Corrected by Rick L. Shepherd, Jul 10 2004

A159878 The digits of Pi whose spellings in English contain no i's.

Original entry on oeis.org

3, 1, 4, 1, 2, 3, 7, 3, 2, 3, 4, 2, 4, 3, 3, 3, 2, 7, 0, 2, 4, 1, 7, 1, 3, 3, 7, 1, 0, 2, 0, 7, 4, 4, 4, 2, 3, 0, 7, 1, 4, 0, 2, 2, 0, 2, 0, 3, 4, 2, 3, 4, 2, 1, 1, 7, 0, 7, 2, 1, 4, 0, 1, 3, 2, 2, 3, 0, 4, 7, 0, 3, 4, 4, 0, 0, 2, 2, 3, 1, 7, 2, 3, 4, 0, 1, 2, 4, 1, 1, 1, 7, 4, 0, 2, 4, 1, 0, 2, 7, 0, 1, 3, 2, 1

Offset: 1

Cino Hilliard, Apr 25 2009

Blind Pi: The series of digits of Pi A000796 after removal of any 5, 6, 8 or 9 (see A095763, A089589).
The difference of the value of this constant to Pi is 0.000355..., compared to a difference of 0.0012... = A003077 for 22/7.
The only other alpha language that has no numbers 0 to 9 with an i is Albanian.
It is natural to ask "is the constant defined in this way irrational, transcendental?"

			Pi = 3.1415... . The digit 5 or five contains an i in the spelling. So 5 is not in the sequence.

Flatten[ RealDigits[Pi, 10, 174][[1]] /. {5 -> {}, 6 -> {}, 8 -> {}, 9 -> {}}] (* Robert G. Wilson v, May 27 2009 *)

blindpi(n) =
{
default(realprecision,1000);
local(pi,x);
pi=Vec(Str(Pi*10^99));
default(realprecision,28);
for(x=1,n,
if(pi[x]=="0"||pi[x]=="1"||pi[x]=="2"||pi[x]=="3"||pi[x]=="4"||pi[x]=="7",
print1(pi[x]",");
);
);
}

Edited by R. J. Mathar, Apr 28 2009

cp's OEIS Frontend

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

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

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

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A008537 Numbers that do not contain the letter 'n'.

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