keyword:word - cp's OEIS frontend

A008522 Numbers whose American English name contains the letter 't'.

2, 3, 8, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77

Offset: 1

N. J. A. Sloane

			8 = eigh{t}.

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A008519 (o), A008520 (e), A008536 (n), A008538 (s), A008540 (f), A008553 (y).

A008522Q[n_]:=StringContainsQ[IntegerName[n,"Words"],"t"];Select[Range[0,200],A008522Q] (* Paolo Xausa, Aug 12 2023 *)

Name edited by Paolo Xausa, Aug 12 2023

A052363 Numbers n whose English name has a greater length (A005589) than any smaller number.

Original entry on oeis.org

0, 3, 11, 13, 17, 23, 73, 101, 103, 111, 113, 117, 123, 173, 323, 373, 1103, 1111, 1113, 1117, 1123, 1173, 1323, 1373, 3323, 3373, 11373, 13323, 13373, 17373, 23323, 23373, 73373, 101373, 103323, 103373, 111373, 113323, 113373, 117373, 123323, 123373, 173373, 323373, 373373

Offset: 1

Allan C. Wechsler, Mar 07 2000

Indices of records in A005589 (which only counts letters, but not spaces and punctuation, in the English name of numbers).

			Note that A052360(373373) = 64 and A005589(373373) = 56.
Sequence A052362 uses A052360 which also counts spaces and dashes, therefore "twenty-one" is in that sequence but not in this one: it uses one more character ('-') but has the same number of letters than "seventeen". - _M. F. Hasler_, Aug 12 2020

Michael S. Branicky, Table of n, a(n) for n = 1..597 (terms < 10^54)
Eric Weisstein's World of Mathematics, Number
Eric Weisstein's World of Mathematics, Large Number
Wikipedia, Names of Large Numbers
Wiktionary, one hundred one (US)
Wiktionary, one hundred and one (UK)
Robert G. Wilson v, American English names for the numbers from 0 to 100999 without spaces or hyphens

Cf. A005589, A052360, A052362.

m=0; for(n=0, 2e6, if(m<A005589(n), m=A005589(n); print1(n", "))) \\ M. F. Hasler, Aug 12 2020

from itertools import count, islice
from num2words import num2words as n2w
def f(n): return sum(1 for c in n2w(n).replace(" and", "") if c.isalpha())
def agen():
    record = 0
    for n in count(0):
        value = f(n)
        if value > record: yield n; record = value
        n += 1
print(list(islice(agen(), 40))) # Michael S. Branicky, Jul 12 2022

Edited by R. J. Mathar and T. D. Noe, Apr 09 2009
Minor edits by Ray Chandler, Jul 22 2009
a(41) and beyond from Michael S. Branicky, Jul 12 2022

A080777 a(n), when spelled in English, is the smallest positive integer with exactly n letters.

Original entry on oeis.org

1, 4, 3, 11, 15, 13, 17, 24, 23, 73, 101, 104, 103, 111, 115, 113, 117, 124, 123, 173, 323, 373, 1104, 1103, 1111, 1115, 1113, 1117, 1124, 1123, 1173, 1323, 1373, 3323, 3373, 11373, 13323, 13373, 17373, 23323, 23373, 73373, 101373, 103323, 103373, 111373

Offset: 3

Peter Kolbus (peter(AT)kolbusfamily.com), Mar 11 2003

In this version 101 is written "one hundred one", etc.

This uses the conventions that "and" is never used and two-digit numbers are not used before "hundred". The sequence is labeled "finite" because there is no widely accepted naming convention for arbitrarily large numbers. - David Wasserman, Dec 20 2004

			The 3rd term has 5 letters; the smallest positive integer with this number of letters is 3 (three).

Hans Havermann, Table of n, a(n) for n = 3..758
Hans Havermann, Growth illustration for this sequence

Cf. A001166, A052196 (the 'largest' analog of this sequence), A084390.

(* Works for a(n) up to 10^k *)
k=5;name[n_]:=IntegerName[n,"Words"];
nameLen[n_]:=StringLength[StringReplace[name[n],{" "-> "","-"-> "",","-> ""}]];
max[n_]:=Max[nameLen/@Range[10^(n-1)+1,10^n]];max10toK=max/@Range[k];
pos[n_Integer/;n>2]:=Position[Sort[Append[max10toK,n]],n,1][[1,1]]-1;
a[n_Integer/;n>2&&n<(10^k)+1]:=Module[{l=10^pos[n]},While[nameLen[l]!=n,l++];l];
a/@Range[3,40] (* Ivan N. Ianakiev, Sep 05 2018 *)

Corrected by James Ong (blackshadowshade(AT)yahoo.com.au), Jun 27 2003
More terms from Brian Galebach, Feb 06 2004
Edited by David Wasserman, Dec 20 2004

A139282 Form a sequence of words as follows: look to the left, towards the beginning of the sequence and write down the number of vowels you see; repeat; then replace the words with the corresponding numbers.

Original entry on oeis.org

0, 2, 3, 5, 7, 9, 11, 14, 18, 22, 24, 27, 30, 31, 34, 37, 40, 41, 44, 47, 50, 51, 54, 57, 60, 61, 64, 67, 70, 72, 75, 79, 83, 87, 91, 95, 99, 103, 110, 116, 124, 132, 139, 147, 155, 163, 171, 180, 187, 196, 204, 210, 215, 222, 228, 235, 242, 248, 255, 262, 268, 275

Offset: 0

N. J. A. Sloane, Jun 08 2008

The sequence of words is: zero, two, three, five, seven, nine, eleven, fourteen, ...

Hyphens and spaces are not counted.

			The second word is "two" (and so a(2)=2), because at the end of the first word we can see two vowels (the vowels in "zero") to the left.

E. Angelini, "Jeux de suites", in Dossier Pour La Science, pp. 32-35, Volume 59 (Jeux math'), April/June 2008, Paris.

For a French version see A139212.

Cross reference corrected by Sean A. Irvine, Mar 15 2010

More terms from Sean A. Irvine, Mar 15 2010

A380248 The order of the 13 cards of one suit such that after the SpellUnder-Down deal the cards are in order; a(n) is the n-th card in the deck.

Original entry on oeis.org

3, 8, 7, 1, 12, 6, 4, 2, 11, 13, 10, 9, 5

Offset: 1

Tanya Khovanova and the MIT PRIMES STEP junior group, Jan 17 2025

Number 1 corresponds to ace, 11 to jack, 12 to queen, 13 to king.
In the SpellUnder-Down deal, we spell the next card, putting a card under for each letter in the name, then we deal the next card. So we start with putting 3 cards under for A-C-E, then deal, then 3 cards under for T-W-O, then deal, then 5 cards under for T-H-R-E-E, then deal. The dealing sequence is highly irregular because it depends on English spelling. The dealing pattern starts: UUUDUUUDUUUUUD.
The sequence is a permutation of 13 numbers.

			The first card dealt is the fourth card in the deck, thus, the fourth card must be an ace.

Cf. A005589, A006257, A225381, A321298, A378635, A380201, A380202, A380204, A380246, A380247.

A001166 Smallest natural number requiring n letters in English.

Original entry on oeis.org

1, 4, 3, 11, 15, 13, 17, 24, 23, 73, 3000, 11000, 15000, 101, 104, 103, 111, 115, 113, 117, 124, 123, 173, 323, 373, 1104, 1103, 1111, 1115, 1113, 1117, 1124, 1123, 1173, 1323, 1373, 3323, 3373, 11373, 13323, 13373, 17373, 23323, 23373, 73373, 101123, 101173, 101323, 101373, 103323, 103373, 111373, 113323, 113373, 117373

Offset: 3

N. J. A. Sloane

In this version 101 is written "one hundred and one", etc.

			For n = 6, the smallest natural number requiring 6 letters in English is "eleven." - _Julia Carrigan_, Jan 19 2024

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Sean A. Irvine, Illustration of terms a(3) through a(75)

Cf. A000916, A014388, A045494, A045495, A080777.

Corrected and extended by Henry Bottomley, Jan 28 2000
Further corrected and extended by Brian Galebach, Feb 06 2004
Further corrected and illustration of terms by Sean A. Irvine, Mar 12 2012

A008536 Numbers whose American English name contains the letter 'n'.

Original entry on oeis.org

1, 7, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 37, 39, 41, 47, 49, 51, 57, 59, 61, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 87, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107

Offset: 1

N. J. A. Sloane

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A008519 (o), A008520 (e), A008522 (t), A008538 (s), A008540 (f), A008553 (y).

A008536Q[n_]:=StringContainsQ[IntegerName[n,"Words"],"n"];Select[Range[0,200],A008536Q] (* Paolo Xausa, Aug 12 2023 *)

Name edited by Paolo Xausa, Aug 12 2023

A031139 Number of letters in English words for months of year.

Original entry on oeis.org

7, 8, 5, 5, 3, 4, 4, 6, 9, 7, 8, 8, 7, 8, 5, 5, 3, 4, 4, 6, 9, 7, 8, 8, 7, 8, 5, 5, 3, 4, 4, 6, 9, 7, 8, 8, 7, 8, 5, 5, 3, 4, 4, 6, 9, 7, 8, 8, 7, 8, 5, 5, 3, 4, 4, 6, 9, 7, 8, 8, 7, 8, 5, 5, 3, 4, 4, 6, 9, 7, 8, 8, 7, 8, 5, 5, 3, 4, 4, 6, 9, 7, 8, 8

Offset: 1

Dmitri Papichev (Dmitri.Papichev(AT)iname.com)

Period 12: repeat [7, 8, 5, 5, 3, 4, 4, 6, 9, 7, 8, 8].

According to the definition this should strictly speaking be finite: there is no 13th month of the year. But for several reasons we prefer to see this as an infinite periodic sequence. - M. F. Hasler, Mar 05 2018

			a(1) = 7 because January has 7 letters.

GCHQ, The GCHQ Puzzle Book, Penguin, 2016. See page 60.

Time and Date, A Calendar website.
Index entries for sequences related to calendars.
Index to 12-periodic sequences.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,1).

Cf. A089746, A161376, A182495.

PadRight[{}, 72, {7, 8, 5, 5, 3, 4, 4, 6, 9, 7, 8, 8}] (* or *)
Array[StringLength@ DateString[DateObject[{0, Mod[#, 12] + 1, 1, 0, 0, 0}, "Month"], {"MonthName"}] &, 72, 0] (* Michael De Vlieger, Feb 25 2018 *)

A031139(n)=digits(879644355878)[12-n%12] \\ M. F. Hasler, Mar 05 2018

From Elmo R. Oliveira, Jul 18 2024: (Start)
G.f.: x*(7 + 8*x + 5*x^2 + 5*x^3 + 3*x^4 + 4*x^5 + 4*x^6 + 6*x^7 + 9*x^8 + 7*x^9 + 8*x^10 + 8*x^11)/(1 - x^12).
a(n) = a(n-12) for n > 12. (End)

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

Eric W. Weisstein, Nov 09 2003

Blind numbers. - Cino Hilliard, May 03 2004

There are 30276 terms, ending in 777777. - Michael S. Branicky, Aug 04 2022

Michael S. Branicky, Table of n, a(n) for n = 1..30276 (full sequence; terms 1..10000 from Reinhard Zumkeller)
Roel and Bas van Dijk, Numerals package, Hackage (Haskell packages).
Eric Weisstein's World of Mathematics, Iban Number
Wikipedia, Names of Large Numbers
Index entries for sequences related to number of letters in n

Cf. A006933 (ban e), A008521 (ban o), 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
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

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

A000852 Numbers beginning with a vowel in English.

Original entry on oeis.org

1, 8, 11, 18, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132

Offset: 1

N. J. A. Sloane

John Cerkan, Table of n, a(n) for n = 1..10000

Cf. A000865, A000873.

cp's OEIS Frontend

A008522 Numbers whose American English name contains the letter 't'.

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A052363 Numbers n whose English name has a greater length (A005589) than any smaller number.

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A080777 a(n), when spelled in English, is the smallest positive integer with exactly n letters.

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A139282 Form a sequence of words as follows: look to the left, towards the beginning of the sequence and write down the number of vowels you see; repeat; then replace the words with the corresponding numbers.

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A380248 The order of the 13 cards of one suit such that after the SpellUnder-Down deal the cards are in order; a(n) is the n-th card in the deck.

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A001166 Smallest natural number requiring n letters in English.

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A008536 Numbers whose American English name contains the letter 'n'.

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Mathematica

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A031139 Number of letters in English words for months of year.

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Mathematica