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

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

1,2

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, ...

Links

Table of n, a(n) for n=1..51.

Example

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).

Prog

(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.

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.

Sequence in context: A368083 A067186 A133675 * A173467 A050122 A179016

Adjacent sequences: A332065 A332066 A332067 * A332069 A332070 A332071

Keyword

nonn,word

Author

M. F. Hasler, Aug 10 2020

Status

approved