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

2, 3, 11, 14, 71, 101, 111, 114, 171, 1071, 1101, 1111, 1114, 1171, 11171, 14171, 71171, 101171, 111171, 114171, 171171, 1071171, 1101171, 1111171, 1114171, 1171171, 11171171, 14171171, 71171171, 101171171, 111171171, 114171171, 171171171, 1071171171, 1101171171

Offset

1,1

Comments

In US English, "101" is written as "one hundred one".

From Michael S. Branicky, Oct 24 2020 (Start)

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.

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).

Also, a(n) = A158352(n) for n >= 3. (proof in A158352).

(End)

Links

Table of n, a(n) for n=1..35.

Eric Weisstein's World of Mathematics, Large Number

Wikipedia, Names of Large Numbers

Wiktionary, one hundred one (US)

Wiktionary, one hundred and one (UK)

Robert G. Wilson v, American English names for the numbers from 0 to 100999 without spaces or hyphens

Example

"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.

Prog

(Python)
from num2words import num2words
def A158353upto(n):
  i, ans = 1, []
  for k in range(1, n+1):
    while sum(1 for c in num2words(i).replace(' and ', '') if c in "aeiouy") != k:
      i += 1
      ans.append(i)
  return ans
print(A158353upto(20)) # Michael S. Branicky, Oct 23 2020

Crossrefs

Cf. A000052, A079741, A158352.

Sequence in context: A182709 A321766 A041029 * A158355 A041235 A036972

Adjacent sequences: A158350 A158351 A158352 * A158354 A158355 A158356

Keyword

nonn,word

Author

Rodolfo Kurchan, Mar 16 2009

Extensions

Edited by Jon E. Schoenfield, Sep 29 2018

a(9) and beyond from Michael S. Branicky, Oct 23 2020

Status

approved