A158352 a(n) is the smallest number whose name in US English contains n vowels.

2, 1, 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

Author

Rodolfo Kurchan, Mar 16 2009

Keywords

• nonn
• word

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) = A158353(n) for n >= 3. Proof. For them to differ after (171)^n, which has 9*n vowels, would require either (i) "one [power name] two" be next, preceding "one [power name] one"), which could only occur if [power name] had 9*n-2 vowels; or (ii) [power name] has > 9*n-2 vowels and a subsequent power name has less (within a range depending on n). Neither case occurs for existing names (see Wikipedia Large numbers link). (End)

Examples

			"twO" has 1 vowel, "OnE" has 2, "ElEvEn" has 3, "fOUrtEEn" has 4, "sEvEntY-OnE" has 5, "OnE hUndrEd OnE" has 6, "OnE hUndrEd ElEvEn" has 7.
		

Links

• 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

Crossrefs

Cf. A000052, A079741, A158353.

Programs

Mathematica

With[{s = Array[StringCount[StringJoin@ Map[If[IntegerQ[#], IntegerName[#], ToString[#]] &, ToExpression@ StringSplit@ IntegerName[#]], {"a", "e", "i", "o", "u", "y"}] &, 10^4]}, Array[FirstPosition[s, #][[1]] &, Max@ s]] (* Michael De Vlieger, Nov 06 2020 *)

Python

from num2words import num2words
def A158352(n):
  i = 1
  while sum(1 for c in num2words(i).replace(' and ', '') if c in "aeiouy")!=n:
    i += 1
  return i
print([A158352(n) for n in range(1,16)]) # Michael S. Branicky, Oct 23 2020

Extensions

Edited by Jon E. Schoenfield, Sep 29 2018

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