This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A332068 #14 Aug 25 2020 06:40:17
%S A332068 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 A332068 66,70,72,73,74,76,77,78,80,82,84,86,3000000,3000002,3000004,3000040,
%U A332068 3000042,3000044,6000000,6000002,6000004,6000040,6000042,6000044,7000000,7000002,7000004
%N A332068 Numbers whose English name has at least two vowels and all the vowels are in alphabetical order.
%C A332068 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 A332068 No number with "hUndrEd", "thoUsAnd", or "One / twO / foUr mIllioN" (or "fIvE, nInE"...) in it has the required property.
%C A332068 The vowels are counted with multiplicity: e.g., "thrEE" with two 'E's is listed.
%C A332068 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 A332068 Numbers 0, 3, 4, ... have the required property, since their English names are "zErO", "thrEE", "fOUr", ...
%e A332068 Numbers 1, 2, 5, ... ("OnE", "twO", "fIvE", ...) don't have the property (vowels in incorrect order or less than two).
%o A332068 (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 A332068 Cf. A052360.
%Y A332068 A095947 \ {10} is the subset of numbers having only vowel E, and more than once.
%Y A332068 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 A332068 See A332069 for numbers having all 5 vowels, in alphabetical order.
%K A332068 nonn,word
%O A332068 1,2
%A A332068 _M. F. Hasler_, Aug 10 2020