A000052 -id:A000052 - cp's OEIS frontend

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

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

A134777 First digit of n alphabetically.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 1, 1, 4, 5, 1, 1, 8, 9, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 3, 1, 3, 3, 4, 5, 6, 7, 8, 9, 4, 4, 4, 4, 4, 5, 4, 4, 8, 4, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 6, 1, 6, 6, 4, 5, 6, 7, 8, 9, 7, 1, 7, 7, 4, 5, 7, 7, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 4, 5, 9, 9, 8, 9, 1, 1, 1, 1, 4

Offset: 0

Rick L. Shepherd, Nov 11 2007

Digits are decimal with names in English (see A000052). A134777(n)=A134778(n) iff n is a repdigit (n=A010785(m)), in which case a(n)=A010888(m), the repeated digit. a(n)=0 only for n=0. a(n)=8 iff n is a member of A011538.

			a(104) = 4 because the digits of 104 are 1 (one), 0 (zero) and 4 (four) and "four" occurs before both "one" and "zero" alphabetically.

Michael S. Branicky, Table of n, a(n) for n = 0..10000

Cf. A134778, A000052, A010785, A010888, A011538.

def alpha(n): return [8, 5, 4, 9, 1, 7, 6, 3, 2, 0].index(n)
def a(n): return sorted(map(int, str(n)), key=alpha)[0]
print([a(n) for n in range(105)]) # Michael S. Branicky, Dec 12 2023

A134778 Last digit of n alphabetically.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 1, 1, 6, 7, 1, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 3, 2, 3, 3, 3, 3, 3, 3, 3, 0, 1, 2, 3, 4, 4, 6, 7, 4, 9, 0, 1, 2, 3, 4, 5, 6, 7, 5, 9, 0, 6, 2, 3, 6, 6, 6, 6, 6, 6, 0, 7, 2, 3, 7, 7, 6, 7, 7, 7, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 9, 9, 6, 7, 9, 9, 0, 0, 0, 0, 0

Offset: 0

Rick L. Shepherd, Nov 11 2007

Digits are decimal with names in English (see A000052). A134778(n)=A134777(n) iff n is a repdigit (n=A010785(m)), in which case a(n)=A010888(m), the repeated digit. a(n)=0 iff n is a member of A011540. a(n)=8 iff n is a member of A002282-{0}.

			a(104) = 0 because the digits of 104 are 1 (one), 0 (zero) and 4 (four) and "zero" occurs after both "four" and "one" alphabetically.

Michael S. Branicky, Table of n, a(n) for n = 0..10000

Cf. A134777, A000052, A010785, A010888, A011540, A002282.

def alpha(n): return [8, 5, 4, 9, 1, 7, 6, 3, 2, 0].index(n)
def a(n): return sorted(map(int, str(n)), key=alpha)[-1]
print([a(n) for n in range(105)]) # Michael S. Branicky, Dec 12 2023

A187876 1-digit numbers arranged in alphabetical order, then the 2-digit numbers arranged in alphabetical order, then the 3-digit numbers, etc. French version.

Original entry on oeis.org

5, 2, 8, 9, 4, 7, 6, 3, 1, 0, 50, 55, 52, 51, 58, 59, 54, 57, 56, 53, 10, 18, 19, 17, 12, 11, 40, 45, 42, 41, 48, 49, 44, 47, 46, 43, 14, 85, 82, 90, 98, 99, 97, 92, 88, 89, 91, 94, 84, 95, 80, 96, 87, 86, 93, 83, 81, 15, 16, 60, 65, 62, 70, 78, 79, 77, 72, 71, 61, 68, 69, 74, 64, 75, 76, 67, 66, 73, 63, 13, 30, 35, 32, 31, 38, 39, 34, 37, 36, 33, 20, 25, 22, 21, 28, 29, 24, 27, 26, 23, 100, 105, 150, 155, 152, 151, 158, 159, 154, 157, 156, 153, 102, 110, 118, 119, 117, 112

Offset: 1

Olivier Gérard, Mar 14 2011

I have used the metropolitan modern French convention (with dashes), spelling 80 as quatre-vingts and 91 as quatre-vingt-onze for instance.
Using the masculine version of each cardinal number.
Another version could use septante/octante/nonante instead of soixante-dix/quatre-vingts/quatre-vingt-dix etc.

			cinq, deux, huit, neuf, quatre, sept, six, trois, un, zéro, cinquante, cinquante-cinq, cinquante-deux, cinquante-et-un, etc.

Sean A. Irvine, Table of n, a(n) for n = 1..1000
Sean A. Irvine, Table of n, a(n) for n = 1..1000 (with names in UTF-8)

Correct version of A001062.

French equivalent of A000052. More comprehensive version of A187875.

Missing 154 inserted by Sean A. Irvine, Apr 29 2019

A036747 The numbers 0-100 in English lexicographic order.

Original entry on oeis.org

8, 18, 80, 88, 85, 84, 89, 81, 87, 86, 83, 82, 11, 15, 50, 58, 55, 54, 59, 51, 57, 56, 53, 52, 5, 40, 48, 45, 44, 49, 41, 47, 46, 43, 42, 4, 14, 9, 19, 90, 98, 95, 94, 99, 91, 97, 96, 93, 92, 1, 100, 7, 17, 70, 78, 75, 74, 79, 71, 77, 76, 73, 72, 6, 16, 60, 68, 65, 64, 69, 61, 67, 66, 63, 62, 10, 13, 30, 38, 35, 34, 39, 31, 37, 36, 33, 32, 3, 12, 20, 28, 25, 24, 29, 21, 27, 26, 23, 22, 2, 0

Offset: 0

David W. Wilson

J. C. Mark and S. Ulam, A memorable memo, in Los Alamos Science, Special Issue, 1987.

Cf. A000052.

The original (incorrect) Mark-Ulam list is given in A261402.

SortBy[Range[0, 100], IntegerName] (* Davin Park, Dec 25 2016 *)

Extended with full list of 101 terms by N. J. A. Sloane, Aug 21 2015

a(76) = 10 inserted by Davin Park, Dec 25 2016

A119796 Zero through ten in alphabetical order of English reverse spelling.

Original entry on oeis.org

3, 9, 1, 5, 10, 7, 0, 2, 4, 8, 6

Offset: 1

Jonathan Vos Post, Jul 30 2006

			a(1) = 3 because EERHT comes alphabetically first.
a(2) = 9 because ENIN comes alphabetically second.
a(3) = 1 because ENO comes alphabetically third.
a(4) = 5 because EVIF comes alphabetically fourth.

Cf. A000052, A004740, A019440, A026081, A001058, A057846, A108067, A072991.

A119898 1-digit numbers arranged in alphabetical order of English spelling reversed, then the 2-digit numbers so arranged, then the 3-digit numbers, etc.

Original entry on oeis.org

3, 9, 1, 5, 7, 0, 2, 4, 8, 6, 93, 53, 83, 73, 23, 33, 43, 63, 99, 59, 89, 79, 29, 39, 49, 69, 91, 51, 81, 71, 21, 31, 41, 61, 95, 55, 85, 75, 25, 35, 45, 65, 12, 19, 15, 18, 17, 13, 14, 16, 10, 11, 97, 57, 87, 77, 27, 37, 47, 67, 92, 52, 82, 72, 22, 32, 42, 62, 94, 54, 84, 74, 24

Offset: 1

Jonathan Vos Post, Aug 01 2006

Analog of A000052 where the alphabetical order is applied not to English name of integer but to the English name whose letters are then reversed.

			Eerht, Enin, Eno, Evif, Neves, Orez, Owt, Ruof, Thgie, Xis;
Eerhtytenin, Eerhtytfif, Eerhtythgie, Eerhtytneves, Eerhtytnewt, Eerhtytriht, Eerhtytrof, Eerhtytxis, Eninytenin, Eninytfif, Eninythgie, Eninytneves, Eninytnewt, Eninytriht, Eninytrof, Eninytxis, Enoytenin, Enoytfif, Enoythgie, Enoytneves, Enoytnewt, Enoytriht, Enoytrof, Enoytxis, Evifytenin, Evifytfif, ...

Cf. A000052, A004740, A019440, A026081, A001058, A057846, A108067, A072991.

f[a_, b_] := Sort@ Table[{ StringReverse[ StringReplace[ IntegerName[h, "Words"], {"\[Hyphen]" -> ""}]], h}, {h, a, b}]; Last /@ Join[f[0, 9], f[10, 99]] (* Giovanni Resta, Jun 13 2016 *)

Data and example corrected by Giovanni Resta, Jun 13 2016

A187875 Numbers from zero to ten, sorted alphabetically by their French name.

Original entry on oeis.org

5, 2, 10, 8, 9, 4, 7, 6, 3, 1, 0

Offset: 1

Latelio(AT)gmail.com and Olivier Gérard, Mar 14 2011

Initials are c,d,d,h,n,q,s,s,t,u,z.

Starting from a larger set would give a different sequence.

			Cinq, deux, dix, huit, neuf, quatre, sept, six, trois, un, zéro.

Thread "Alphabète" - Oulipo mailing list, March 22 2011

French equivalent of A072991. See also A000052.

A261402 The Mark-Ulam sequence: an erroneous version of A036747.

Original entry on oeis.org

12, 8, 18, 80, 88, 85, 84, 89, 81, 87, 86, 83, 82, 11, 15, 50, 58, 55, 54, 59, 51, 57, 56, 53, 52, 5, 40, 48, 45, 44, 49, 41, 47, 46, 43, 42, 4, 14, 9, 19, 90, 98, 95, 94, 99, 91, 97, 96, 93, 92, 1, 100, 7, 17, 70, 78, 75, 74, 79, 71, 77, 76, 73, 72, 6, 16, 60, 68, 65, 64, 69, 61, 67, 66, 63, 62, 13, 30, 38, 35, 34, 39, 31, 37, 36, 33, 32, 3, 12, 20, 28, 25, 24, 29, 21, 27, 26, 23, 22, 2, 0

Offset: 1

Michel Marcus and N. J. A. Sloane, Aug 21 2015

Note that 10 is missing and 12 appears twice (the first 12 refers to "a dozen").

J. C. Mark and S. Ulam, A memorable memo, in Los Alamos Science, Special Issue, 1987.

Cf. A000052, A036747.

A063761 Arrange 1-digit numbers in alphabetical order in Italian, then the 2-digit numbers, then the 3-digit numbers, etc.

Original entry on oeis.org

5, 2, 9, 8, 4, 6, 7, 3, 1, 0, 50, 55, 52, 59, 54, 56, 57, 53, 58, 51, 19, 17, 18, 10, 12, 90, 95, 92, 99, 94, 96, 97, 93, 98, 91, 80, 85, 82, 89, 84, 86, 87, 83, 88, 81, 40, 45, 42, 49, 44, 46, 47, 43, 48, 41, 14, 15, 16, 60, 65, 62, 69, 64, 66, 67, 63, 68, 61, 70, 75, 72, 79, 74, 76, 77, 73, 78, 71, 13, 30, 35, 32, 39, 34, 36, 37, 33, 38, 31, 11, 20, 25, 22, 29, 24, 26, 27, 23, 28, 21

Offset: 0

Roberto Callegari (calleg(AT)dnet.it), Aug 14 2001

			5 = cinque, 2 = due, 9 = nove, 8 = otto, ...

Cf. A000052.

Duplicate 99 removed and extended to all 2-digit numbers by Sean A. Irvine, May 12 2023

cp's OEIS Frontend

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

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A134777 First digit of n alphabetically.

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A134778 Last digit of n alphabetically.

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A187876 1-digit numbers arranged in alphabetical order, then the 2-digit numbers arranged in alphabetical order, then the 3-digit numbers, etc. French version.

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A036747 The numbers 0-100 in English lexicographic order.

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A119796 Zero through ten in alphabetical order of English reverse spelling.

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A119898 1-digit numbers arranged in alphabetical order of English spelling reversed, then the 2-digit numbers so arranged, then the 3-digit numbers, etc.

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Mathematica

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A187875 Numbers from zero to ten, sorted alphabetically by their French name.

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A261402 The Mark-Ulam sequence: an erroneous version of A036747.

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