A058179 -id:A058179 - cp's OEIS frontend

A037196 Number of vowels in the American English name of n.

2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 3, 2, 3, 4, 3, 3, 4, 4, 4, 1, 3, 2, 3, 3, 3, 2, 3, 3, 3, 1, 3, 2, 3, 3, 3, 2, 3, 3, 3, 1, 3, 2, 3, 3, 3, 2, 3, 3, 3, 1, 3, 2, 3, 3, 3, 2, 3, 3, 3, 1, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 4, 3, 4, 4, 4, 3, 4, 4, 4, 2, 4, 3, 4, 4, 4, 3, 4, 4, 4, 2, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 6, 5, 6, 6

Offset: 0

N. J. A. Sloane

"American English" means that there is no "and" in the names of numbers, cf. example. - M. F. Hasler, Aug 26 2020

			a(20) = 1 for "twEnty" with 1 vowel: 'y' does not count.
a(101) = 6 for "OnE hUndrEd OnE" with 6 vowels: no "and" as in the "British" variant "one hundred and one" which would have 7 vowels.

Cf. A005589, A052360 (number of letters in English name of numbers with/without spaces and dashes).

Sequences related to vowels: A102869, A158352, A158354 (smallest number with n [distinct] vowels in AE / BE), A158353, A158355 (ditto, increasing), A058179 (all 5 vowels), A058180 (ditto, exactly once), A000852, A000861 (start/end with vowel), A019270, A080518 (self-describing), A059437, A079741, A152592, A174879, A241858, A332068, A332069.

vowels=Vec("aeiou"); apply( {A037196(n)=#[c|c<-Vec(English(n)),setsearch(vowels,c)]}, [0..104]) \\ see A052360 for English(). - M. F. Hasler, Aug 26 2020

from num2words import num2words
def a(n): return sum(1 for c in num2words(n).replace(" and", "") if c in "aeiou")
print([a(n) for n in range(105)]) # Michael S. Branicky, Mar 23 2025

More terms from Larry Reeves (larryr(AT)acm.org), Sep 25 2000
Name edited and crossrefs added by M. F. Hasler, Aug 26 2020
a(19)=4 corrected by Sean A. Irvine, Dec 16 2020

A058180 Numbers whose English names include all five vowels exactly once.

Original entry on oeis.org

206, 230, 250, 260, 602, 640, 5000, 8000, 9000, 26000, 80000, 90000

Offset: 1

Stewart Gordon, Nov 14 2000

			206 = two hundred and six 80000 = eighty thousand

GCHQ, The GCHQ Puzzle Book II, Penguin, 2018. See question 189(b).

Cf. A058179.

A332068 Numbers whose English name has at least two vowels and all the vowels are in alphabetical order.

Original entry on oeis.org

0, 3, 4, 7, 8, 11, 12, 17, 22, 23, 24, 26, 27, 28, 32, 34, 36, 42, 44, 52, 54, 56, 62, 64, 66, 70, 72, 73, 74, 76, 77, 78, 80, 82, 84, 86, 3000000, 3000002, 3000004, 3000040, 3000042, 3000044, 6000000, 6000002, 6000004, 6000040, 6000042, 6000044, 7000000, 7000002, 7000004

Offset: 1

M. F. Hasler, Aug 10 2020

Here (as in most OEIS sequences) vowel means one of the five letters A, E, I, O or U. (One could imagine variants that use Y, too.)
No number with "hUndrEd", "thoUsAnd", or "One / twO / foUr mIllioN" (or "fIvE, nInE"...) in it has the required property.
The vowels are counted with multiplicity: e.g., "thrEE" with two 'E's is listed.
The subsequence of numbers which have at least two distinct vowels in alphabetical order is 0, 4, 8, 22, 24, 26, 28, 32, 34, 44, 52, 54, 62, 64, 72, 74, 76, 78, 80, 82, 84, 86, 3000000, ...

			Numbers 0, 3, 4, ... have the required property, since their English names are "zErO", "thrEE", "fOUr", ...
Numbers 1, 2, 5, ... ("OnE", "twO", "fIvE", ...) don't have the property (vowels in incorrect order or less than two).

Cf. A052360.
A095947 \ {10} is the subset of numbers having only vowel E, and more than once.
Sequences related to vowels: A037196 (# vowels), A102869, A158352, A158354 (smallest number with n [distinct] vowels in AE / BE), A158353, A158355 (ditto, increasing), A058179 (all 5 vowels), A058180 (ditto, exactly once), A000852, A000861 (start/end with vowel), A019270, A080518 (self-describing), A059437, A079741, A152592, A174879, A241858.
See A332069 for numbers having all 5 vowels, in alphabetical order.

select( {is_A332068(n,v=Vec("aeiou"))=#(t=[c|c<-Vec(English(n)),setsearch(v,c)])>1&&t==vecsort(t)}, [0..999]) \\ See A052360 for English(). Insert "Set" after '#' to get the subset of numbers with > 1 distinct vowels.

A332069 Numbers whose American English name contains all 5 vowels in alphabetical order.

Original entry on oeis.org

1084, 1134, 1154, 1164, 1184, 1194, 1234, 1254, 1264, 1284, 1294, 1334, 1354, 1364, 1384, 1394, 1434, 1454, 1464, 1484, 1494, 1534, 1554, 1564, 1584, 1594, 1634, 1654, 1664, 1684, 1694, 1734, 1754, 1764, 1784, 1794, 1804, 1814, 1824, 1834, 1844, 1854, 1864, 1874, 1884, 1894

Offset: 1

M. F. Hasler, Aug 10 2020

The name of the number may contain other vowels (A, E, I, O or U) in any place and order. "American English" means that no "and" is used, e.g., 101 = "one hundred one".
Therefore (and because 1000 = "thousAnd" is the least number using the letter "A"), for any term a(n) < 10^4, the number a(n) + x*10^4 is also in the sequence for any x > 0, and so is any number a(n)*10^(6k) + m, m < 10^(6k), k > 0. (The statement isn't true with x*10^3: for example 1084 + 999000 does not have the letter "A".)
In French, 92 ("quAtrE-vIngt dOUze") has the property, and as a consequence the corresponding sequence consists mainly of 92 + x*100 with any x >= 0, and 472 + x*1000 with any x >= 0 ("quAtrE cent soIxante-dOUze"); there is no other term below 4000, from where on others (4012, 4061, 4062, ...) come into play.
In German, the first number to have an 'o' is "Million". Since the 'I' must be preceded by 'A' and 'E', the corresponding sequence would start only after 18*10^6: 18000005, 18000009, 18000015, 18000019, 18000021, 18000022, ...

			1084 is "(one) thousAnd EIghty fOUr". This is the smallest number whose English name contains all 5 vowels A, E, I, O, U in this order, therefore a(1) = 1084.

Anugata Sarkar, in reply to: What are some mind-blowing facts about mathematics?, quora.com, April / Oct. 2019.

Cf. A052360.
Sequences related to vowels: A037196 (# vowels), A102869, A158352, A158354 (smallest number with n [distinct] vowels in AE / BE), A158353, A158355 (ditto, increasing), A058179 (all 5 vowels), A058180 (ditto, exactly once), A000852, A000861 (start/end with vowel), A019270, A080518 (self-describing), A059437, A079741, A152592, A174879, A241858.
Cf. A332068 (also based on the order of vowels in the English name of numbers).

vowels=Vec("aeiou"); (isSubseq(a,b)=forvec(v=vector(#a,i,[i,#b]),vecextract(b,v)==a&&return(1),2)); select( {is_A332069(n)=#Set(n=[c|c<-Vec(English(n)),setsearch(vowels,c)])>4&&isSubseq(vowels,n)}, [0..2000]) \\ See A052360 for English().

A192295 Number of distinct consonants in the English name of n.

Original entry on oeis.org

2, 1, 2, 3, 2, 2, 2, 3, 3, 1, 2, 3, 4, 4, 4, 3, 4, 4, 4, 2, 4, 4, 4, 6, 6, 6, 6, 6, 6, 4, 4, 5, 5, 4, 5, 6, 6, 7, 5, 5, 4, 5, 5, 5, 4, 5, 6, 7, 6, 5, 3, 4, 4, 5, 4, 4, 5, 6, 5, 4, 4, 5, 5, 6, 6, 6, 4, 6, 6, 5, 5, 5, 6, 7, 7, 6, 6, 5, 7, 5, 4, 5, 5, 5, 6, 6, 6, 7, 4, 5, 3, 3, 4, 5, 5, 5, 5, 5, 5, 3, 4, 4, 6, 5, 5

Offset: 0

Kausthub Gudipati, Jun 27 2011

First differs from A037195 at the ninth term.
The letter "y" is here considered a consonant regardless of its usage in the word(s).
The maximum number of distinct vowels that can occur in the English name of n is 5, which occurs for n in A058179. - Jonathan Vos Post, Jul 12 2011

			a(13) = 4 because the distinct consonants present in THIRTEEN are T, H, R and N.
a(9) = 1 because N is the only consonant present in NINE.

Michael De Vlieger, Table of n, a(n) for n = 0..10000

Cf. A037195, A037196 (number of vowels in n), A058179 (numbers whose English names include all five vowels at least once).

Array[Length@ Union@ Select[Characters@ IntegerName@ #, And[LetterQ@ #, FreeQ[{97, 101, 105, 111, 117}, ToCharacterCode[#][[1]]]] &] &, 105, 0] (* Michael De Vlieger, Feb 15 2020 *)

More terms from Michael De Vlieger, Feb 15 2020

A161378 Numbers whose Spanish names include all five vowels at least once.

Original entry on oeis.org

24, 31, 34, 45, 51, 52, 54, 55, 58, 104, 124, 131, 134, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 161, 164, 169, 171, 174, 179, 181, 184, 189, 191, 194, 199, 204, 224, 231, 234, 239, 240, 241, 242

Offset: 1

Claudio Meller, Jun 08 2009

Cf. A058179.

cp's OEIS Frontend

A037196 Number of vowels in the American English name of n.

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A058180 Numbers whose English names include all five vowels exactly once.

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A332068 Numbers whose English name has at least two vowels and all the vowels are in alphabetical order.

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A332069 Numbers whose American English name contains all 5 vowels in alphabetical order.

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PARI

A192295 Number of distinct consonants in the English name of n.

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Mathematica

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A161378 Numbers whose Spanish names include all five vowels at least once.

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