cp's OEIS Frontend

A158353 a(n) is the smallest number greater than a(n-1) whose name in US English contains n vowels.

%I A158353 #32 Dec 04 2020 19:38:26
%S A158353 2,3,11,14,71,101,111,114,171,1071,1101,1111,1114,1171,11171,14171,
%T A158353 71171,101171,111171,114171,171171,1071171,1101171,1111171,1114171,
%U A158353 1171171,11171171,14171171,71171171,101171171,111171171,114171171,171171171,1071171171,1101171171
%N A158353 a(n) is the smallest number greater than a(n-1) whose name in US English contains n vowels.
%C A158353 In US English, "101" is written as "one hundred one".
%C A158353 From _Michael S. Branicky_, Oct 24 2020 (Start)
%C A158353 The sequence counts vowels by counting the instances of the letters 'a', 'e', 'i', 'o', 'u', and 'y' (see Example). If 'y' were not included, then a(5) = 102 ("OnE hUndrEd twO") is the first among subsequent value changes.
%C A158353 In extending the sequence to large numbers, the "American system" (Weisstein link), also known as the "short scale" (Wikipedia link), was used. Also, the common written form is adopted ("one thousand one hundred seventeen" not "eleven hundred seventeen"; Wilson link).
%C A158353 Also, a(n) = A158352(n) for n >= 3. (proof in A158352).
%C A158353 (End)
%H A158353 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LargeNumber.html">Large Number</a>
%H A158353 Wikipedia, <a href="https://en.wikipedia.org/wiki/Names_of_large_numbers">Names of Large Numbers</a>
%H A158353 Wiktionary, <a href="https://en.wiktionary.org/wiki/one_hundred_one">one hundred one</a> (US)
%H A158353 Wiktionary, <a href="https://en.wiktionary.org/wiki/one_hundred_and_one">one hundred and one</a> (UK)
%H A158353 Robert G. Wilson v, <a href="https://oeis.org/A001477/a001477.txt">American English names for the numbers from 0 to 100999 without spaces or hyphens</a>
%e A158353 "twO" has 1 vowel, "thrEE" has 2, "ElEvEn" has 3, "fOUrtEEn" has 4, "sEvEntY-OnE" has 5, "OnE hUndrEd OnE" has 6, "OnE hUndrEd ElEvEn" has 7.
%o A158353 (Python)
%o A158353 from num2words import num2words
%o A158353 def A158353upto(n):
%o A158353   i, ans = 1, []
%o A158353   for k in range(1, n+1):
%o A158353     while sum(1 for c in num2words(i).replace(' and ', '') if c in "aeiouy") != k:
%o A158353       i += 1
%o A158353       ans.append(i)
%o A158353   return ans
%o A158353 print(A158353upto(20)) # _Michael S. Branicky_, Oct 23 2020
%Y A158353 Cf. A000052, A079741, A158352.
%K A158353 nonn,word
%O A158353 1,1
%A A158353 _Rodolfo Kurchan_, Mar 16 2009
%E A158353 Edited by _Jon E. Schoenfield_, Sep 29 2018
%E A158353 a(9) and beyond from _Michael S. Branicky_, Oct 23 2020