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

1,1

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) = 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)

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

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 *)

Prog

(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

Crossrefs

Cf. A000052, A079741, A158353.

Sequence in context: A295852 A088587 A305711 * A158354 A055459 A080958

Adjacent sequences: A158349 A158350 A158351 * A158353 A158354 A158355

Keyword

nonn,word

Author

Rodolfo Kurchan, Mar 16 2009

Extensions

Edited by Jon E. Schoenfield, Sep 29 2018

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

Status

approved