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 1-5 of 5 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

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

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

A073416 Harmless numbers: numbers without a, h, m or r.

Original entry on oeis.org

1, 2, 5, 6, 7, 9, 10, 11, 12, 15, 16, 17, 19, 20, 21, 22, 25, 26, 27, 29, 50, 51, 52, 55, 56, 57, 59, 60, 61, 62, 65, 66, 67, 69, 70, 71, 72, 75, 76, 77, 79, 90, 91, 92, 95, 96, 97, 99, 1000000000, 1000000001, 1000000002
Offset: 1

Views

Author

Michael Joseph Halm, Aug 23 2002

Keywords

Comments

These number differ from A039135 (numbers with same number of 3's and 4's) only in the 17th term and from A072957 (urban numbers without r or u) in the 64th term.

Examples

			a(3) = 5 because 5 is the third integer without an a, h, m or r.

References

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

Crossrefs

Cf. A039135, A072957.

Extensions

Numbers containing 8 (eight) removed by Sean A. Irvine, Nov 28 2024
Showing 1-5 of 5 results.

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

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