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%I #21 Sep 19 2020 18:02:17
%S 1084,1134,1154,1164,1184,1194,1234,1254,1264,1284,1294,1334,1354,
%T 1364,1384,1394,1434,1454,1464,1484,1494,1534,1554,1564,1584,1594,
%U 1634,1654,1664,1684,1694,1734,1754,1764,1784,1794,1804,1814,1824,1834,1844,1854,1864,1874,1884,1894
%N Numbers whose American English name contains all 5 vowels in alphabetical order.
%C 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".
%C 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".)
%C 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.
%C 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, ...
%H Anugata Sarkar, in reply to: <a href="https://www.quora.com/What-are-some-mind-blowing-facts-about-mathematics">What are some mind-blowing facts about mathematics?</a>, quora.com, April / Oct. 2019.
%e 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.
%o (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().
%Y Cf. A052360.
%Y 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.
%Y Cf. A332068 (also based on the order of vowels in the English name of numbers).
%K nonn,word
%O 1,1
%A _M. F. Hasler_, Aug 10 2020
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