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%I #14 Aug 25 2020 06:40:17
%S 0,3,4,7,8,11,12,17,22,23,24,26,27,28,32,34,36,42,44,52,54,56,62,64,
%T 66,70,72,73,74,76,77,78,80,82,84,86,3000000,3000002,3000004,3000040,
%U 3000042,3000044,6000000,6000002,6000004,6000040,6000042,6000044,7000000,7000002,7000004
%N Numbers whose English name has at least two vowels and all the vowels are in alphabetical order.
%C 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.)
%C No number with "hUndrEd", "thoUsAnd", or "One / twO / foUr mIllioN" (or "fIvE, nInE"...) in it has the required property.
%C The vowels are counted with multiplicity: e.g., "thrEE" with two 'E's is listed.
%C 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, ...
%e Numbers 0, 3, 4, ... have the required property, since their English names are "zErO", "thrEE", "fOUr", ...
%e Numbers 1, 2, 5, ... ("OnE", "twO", "fIvE", ...) don't have the property (vowels in incorrect order or less than two).
%o (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.
%Y Cf. A052360.
%Y A095947 \ {10} is the subset of numbers having only vowel E, and more than once.
%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 See A332069 for numbers having all 5 vowels, in alphabetical order.
%K nonn,word
%O 1,2
%A _M. F. Hasler_, Aug 10 2020
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