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A332069 Numbers whose American English name contains all 5 vowels in alphabetical order. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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, ...

LINKS

Table of n, a(n) for n=1..46.

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

EXAMPLE

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.

PROG

(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().

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).

Sequence in context: A220687 A188240 A165809 * A237804 A010091 A206630

Adjacent sequences:  A332066 A332067 A332068 * A332070 A332071 A332072

KEYWORD

nonn,word

AUTHOR

M. F. Hasler, Aug 10 2020

STATUS

approved

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Last modified August 10 00:32 EDT 2022. Contains 356026 sequences. (Running on oeis4.)