A006933 -id:A006933 - cp's OEIS frontend

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

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

A036448 Smallest positive number containing n e's when spelled out in US English.

Original entry on oeis.org

2, 1, 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, 3317317317317

Offset: 0

Rodolfo Kurchan

From Michael S. Branicky, Oct 24 2020: (Start)
"US English" connotes that no "and" is used ("one hundred one") and, importantly here, that the names of large numbers follow the "American system" (Weisstein link), also known as the short scale (Wikipedia link). The previous a(8) and a(9) were based on "eleven hundred and seventeen" and "seventeen hundred and seventeen", which are less common written forms (Wikipedia English numbers link). To make the sequence precise, the common written form is adopted ("one thousand one hundred seventeen"; Wilson link; A000052 Example). Thus, a(n) is the least m such that A085513(m)=n.
The sequence follows the pattern of 1(317)^n, 3(317)^n, 11(317)^n, 17(317)^n, 111(317)^n, 117(317)^n, 317(317)^n for n = 0 through 7 and whenever the largest named power has no "e". a(50) > 10^21 = "one sextillion" which is the first power name that has an "e", breaking the pattern. In that case, a(50) = 1117(317)^6 and a(51) = 1(317)^7. Whenever the largest power has 1 "e" it follows this pattern. If it has m>1 "e"'s, the first block of three is shifted lower to a(7-m). See Wikipedia link for Names of large numbers for power names.
(End)

			One has 1 e.
Three has 2 e's.

Rodolfo Marcelo Kurchan, Problem 1882, Another Number Sequence, Journal of Recreational Mathematics, vol. 23, number 2, p. 141.

Eric Weisstein's World of Mathematics, Large Number
Wikipedia, English numerals
Wikipedia, Names of Large Numbers
Robert G. Wilson v, American English names for the numbers from 0 to 100999 without spaces or hyphens

Cf. A000027, A000052, A001477, A005589, A006933, A037196, A085513.

from num2words import num2words
def A036448(n):
    i = 1
    while num2words(i).count("e")!=n:
        i += 1
    return i
print([A036448(n) for n in range(1,12)]) # Michael S. Branicky, Oct 23 2020

a(8)-a(9) changed and a(11)-a(30) added by Michael S. Branicky, Oct 23 2020

a(0)=2 inserted by Sean A. Irvine, Nov 02 2020

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

A349887 Numbers which, when written in English, contain exactly one instance of the letter E.

Original entry on oeis.org

0, 1, 5, 8, 9, 10, 20, 22, 24, 26, 31, 35, 38, 39, 41, 45, 48, 49, 51, 55, 58, 59, 61, 65, 68, 69, 80, 82, 84, 86, 90, 92, 94, 96, 200, 202, 204, 206, 230, 232, 234, 236, 240, 242, 244, 246, 250, 252, 254, 256, 260, 262, 264, 266, 400, 402, 404, 406, 430, 432, 434, 436

Offset: 1

Eric Angelini, Dec 04 2021

			ZERO has one E, ONE also, but not TWO (no E) nor THREE (2 Es).

Cf. A006933 ('Eban' numbers).

from num2words import num2words
def ok(n): return num2words(n).count("e") == 1
print([k for k in range(667) if ok(k)]) # Michael S. Branicky, Dec 04 2021

A349888 Numbers which, when written in English, contain exactly two instances of the letter E.

Original entry on oeis.org

3, 7, 12, 13, 14, 15, 16, 21, 25, 28, 29, 33, 37, 43, 47, 53, 57, 63, 67, 70, 72, 74, 76, 81, 85, 88, 89, 91, 95, 98, 99, 100, 102, 104, 106, 130, 132, 134, 136, 140, 142, 144, 146, 150, 152, 154, 156, 160, 162, 164, 166, 201, 205, 208, 209, 210, 220, 222, 224, 226, 231, 235, 238, 239

Offset: 1

Eric Angelini, Dec 04 2021

			THREE has two Es (and is thus in the sequence), FOUR has no E, FIVE has only one, SIX has none, SEVEN has two Es (and is thus in the sequence). Etc.

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

Cf. A006933 ('Eban' numbers) and A349887 (exactly one instance).

from num2words import num2words
def ok(n): return num2words(n).count("e") == 2
print([k for k in range(311) if ok(k)]) # Michael S. Branicky, Feb 19 2022

a(7) = 16 inserted by Michael S. Branicky, Feb 19 2022

A114644 Numbers with no "e" in Dutch.

Original entry on oeis.org

0, 5, 8, 12, 20, 50, 80, 5000000000, 8000000000, 12000000000, 20000000000, 50000000000, 80000000000

Offset: 1

N. J. A. Sloane, Feb 18 2006

			Een, twee, drie, vier, VIJF, zes, zeven, ACHT, negen, tien, elf, TWAALF, dertien, ..., TWINTIG, eenentwintig, twee-en-twintig, ..., dertig, eenendertig ... VIJFTIG, ..., TACHTIG, ..., honderd, honderdeen, ...

Heard over coffee at the Computers in Scientific Discovery meeting in Ghent, Feb 02 2006

See A115072 for another version. Cf. A006933 (the eban numbers).

A115072 Numbers with no "e" in Dutch (Miljard without "een").

Original entry on oeis.org

0, 5, 8, 12, 20, 50, 80, 1000000000, 5000000000, 8000000000, 12000000000, 20000000000, 50000000000, 80000000000

Offset: 1

N. J. A. Sloane, Mar 03 2006

			Een, twee, drie, vier, VIJF, zes, zeven, ACHT, negen, tien, elf, TWAALF, dertien, ..., TWINTIG, eenentwintig, twee-en-twintig, ..., dertig, eenendertig ... VIJFTIG, ..., TACHTIG, ..., honderd, honderdeen, ...

See A114644 for another version. Cf. A006933 (the eban numbers).

A287876 Numbers in Hebrew that do not contain the letter ayin.

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 8, 30, 31, 32, 33, 35, 36, 38, 50, 51, 52, 53, 55, 56, 58, 60, 61, 62, 63, 65, 66, 68, 80, 81, 82, 83, 85, 86, 88, 100, 101, 102, 103, 105, 106, 108, 130, 131, 132, 133, 135, 136, 138, 150, 151, 152, 153, 155, 156, 158, 160, 161, 162, 163, 165, 166, 168, 180, 181, 182, 183, 185, 186, 188, 200

Offset: 1

Na'ama Y. Av-Shalom, Jun 15 2017

Suggested by the "Eban numbers", A006933, and, inspired by that name, could also be called the "Eyes shut" sequence, since ayin also means "eye" in Hebrew.

If the OEIS permitted non-ASCII characters, another name would be the עban numbers.

Cf. A006933, A014254.

Corrected and extended by Nathan Fox, Jun 15 2017

A322033 Numbers which when written in German do not contain the letter "e".

Original entry on oeis.org

0, 5, 8, 12, 20, 25, 28, 50, 55, 58, 80, 85, 88

Offset: 1

N. J. A. Sloane, Nov 27 2018

The full list of terms is shown.

Wolfram Stahl, comment following the Numberphile video Brady Haran and N. J. A. Sloane, What Number Comes Next?, Nov 2018

An analog of A006933.

A092752 Numbers which in Portuguese contain no e.

Original entry on oeis.org

1, 2, 4, 5, 8, 30, 1000, 2000, 4000, 5000, 8000, 30000, 1000000, 1000000000000

Offset: 1

Jorge Coveiro, Apr 12 2004

			1 = um
2 = dois
4 = quatro
5 = cinco
8 = oito
30 = trinta

Cf. A006933.

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Python

Extensions

A036448 Smallest positive number containing n e's when spelled out in US English.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Python

Extensions

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Formula

Extensions

A349887 Numbers which, when written in English, contain exactly one instance of the letter E.

Views

Author

Keywords

Examples

Crossrefs

Programs

Python

A349888 Numbers which, when written in English, contain exactly two instances of the letter E.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

Extensions

A114644 Numbers with no "e" in Dutch.

Views

Author

Keywords

Examples

References

Crossrefs

A115072 Numbers with no "e" in Dutch (Miljard without "een").

Views

Author

Keywords

Examples

Crossrefs

A287876 Numbers in Hebrew that do not contain the letter ayin.

Views

Author

Keywords

Comments

Crossrefs

Extensions

A322033 Numbers which when written in German do not contain the letter "e".

Views

Author

Keywords

Comments

Links