cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

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

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Comments

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

Examples

			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.

References

  • 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).

Links

Crossrefs

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').

Programs

  • 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
-- Reinhard Zumkeller, Jan 23 2015
  • 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
  • PARI
    is(n)=!setsearch(Set(Vec(English(n))), "e") \\ See A052360 for English(). - M. F. Hasler, Apr 01 2019
  • Python
    from num2words import num2words
[n for n in range(6001) if 'e' not in num2words(n)] # Indranil Ghosh, Jul 05 2017

Extensions

More terms from WG Zeist, Aug 28 2012
More cross-references from M. F. Hasler, Apr 01 2019

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

Views

Author

Eric W. Weisstein, Nov 09 2003

Keywords

Comments

Blind numbers. - Cino Hilliard, May 03 2004
There are 30276 terms, ending in 777777. - Michael S. Branicky, Aug 04 2022

Links

Crossrefs

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

Programs

  • Haskell
    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
  • Python
    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

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

Views

Author

N. J. A. Sloane

Keywords

Comments

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

Links

Crossrefs

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

Programs

  • Haskell
    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
  • Python
    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

Views

Author

N. J. A. Sloane

Keywords

Comments

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

Links

Crossrefs

Cf. A006933 (ban e), A089589 (ban i), A008521 (ban o), A089590 (ban u).
Complement of A008522.

Programs

  • Haskell
    -- 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
  • Python
    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

Extensions

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

Views

Author

Michael Joseph Halm, Aug 13 2002

Keywords

References

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

Links

Crossrefs

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').

Programs

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

Views

Author

Michael Joseph Halm, Aug 13 2002

Keywords

References

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

Links

Crossrefs

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').

Programs

  • PARI
    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
  • Python
    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

Extensions

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

Views

Author

N. J. A. Sloane

Keywords

Comments

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)

Links

Crossrefs

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).

Programs

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

Extensions

Edited by M. F. Hasler, Apr 01 2019

A072955 Suburban numbers: without b, r, s or u.

Original entry on oeis.org

1, 2, 5, 8, 9, 10, 11, 12, 15, 18, 19, 20, 21, 22, 25, 28, 29, 50, 51, 52, 55, 58, 59, 80, 81, 82, 85, 88, 89, 90, 91, 92, 95, 98, 99, 1000000, 1000001, 1000002, 1000005, 1000008, 1000009, 1000010, 1000011, 1000012, 1000015, 1000018, 1000019, 1000020
Offset: 1

Views

Author

Michael Joseph Halm, Aug 13 2002

Keywords

References

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

Links

Crossrefs

Cf. A089590, A072956, A072957.

Programs

  • Python
    from num2words import num2words
from itertools import islice, product
def ok(n): return set(num2words(n)) & {"b", "r", "s", "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:]) & {"b", "r", "s", "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
Showing 1-8 of 8 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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