A321676 a(1)=1; for n > 1, a(n) is a(n-1) plus the number of vowels in the name of a(n-1) in US English.

1, 3, 5, 7, 9, 11, 14, 18, 22, 24, 27, 30, 31, 34, 37, 40, 41, 44, 47, 50, 51, 54, 57, 60, 61, 64, 67, 70, 72, 75, 79, 83, 87, 91, 95, 99, 103, 109, 115, 122, 128, 135, 142, 148, 155, 162, 168, 175, 183, 191, 199, 207, 212, 217, 224, 230, 234, 240, 244, 250

Offset: 1

Author

Andrew Toothill, Dec 02 2018

Keywords

• nonn
• word
• easy

Comments

This sequence takes into account the numbers written as words; for example, "fifty-seven" contains three vowels, so 3 is added to 57 to create the next term. The word "and" is not included in US English (cf. A158352), so 115 is written as "one hundred fifteen". This sequence is puzzling as it shares its first 6 terms with the odd numbers before jumping to 14, then 18. When only given the first 8 terms it can be very difficult to spot the rule.

Assumes "y" in e.g. "fifty" is not a vowel. - Chai Wah Wu, Dec 17 2018

Crossrefs

Cf. A005589, A037196, A139282, A158352.

Programs

Mathematica

vowelCount[n_] := StringCount[IntegerName[n, "Words"], {"a","e","i","o","u"}]; f[n_] := n + vowelCount[n]; NestList[f, 1, 100] (* Amiram Eldar, Dec 10 2018 *)

Python

from itertools import accumulate, repeat
from num2words import num2words
A321676_list = list(accumulate(repeat(1,100), lambda x, : x+sum(num2words(x).count(d) for d in 'aeiou'))) # _Chai Wah Wu, Dec 17 2018

Formula

a(n) = A139282(n) for n >= 2. - Chai Wah Wu, Dec 17 2018

Extensions

More terms from Amiram Eldar, Dec 10 2018