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 1-3 of 3 results.

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

Original entry on oeis.org

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

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Author

N. J. A. Sloane

Keywords

Comments

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

Examples

			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.

Crossrefs

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.

Programs

  • PARI
    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
  • Python
    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

Extensions

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

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

Views

Author

M. F. Hasler, Aug 10 2020

Keywords

Comments

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, ...

Examples

			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).

Crossrefs

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.

Programs

  • PARI
    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

Views

Author

M. F. Hasler, Aug 10 2020

Keywords

Comments

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, ...

Examples

			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.

Links

Crossrefs

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).

Programs

  • PARI
    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().
Showing 1-3 of 3 results.

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