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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
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
KEYWORD
nonn,word
AUTHOR
M. F. Hasler, Aug 10 2020
STATUS
approved

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Last modified June 24 23:28 EDT 2024. Contains 373691 sequences. (Running on oeis4.)