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Troublemaking Sequence (Posted on 2025-04-15) Difficulty: 3 of 5
The first element is chosen as 1, then the rest of the sequence is determined by a simple rule.
What integer comes next?

Hint: there are two possible answers depending on how one defines a key word in the simple rule.
The title is also a hint.

1, 3, 5, 7, 9, 11, 14, 18, 22, __

See The Solution Submitted by Larry    
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Comments: ( Back to comment list | You must be logged in to post comments.)
re: Resolution in the formula Comment 4 of 4 |
(In reply to Resolution in the formula by Jer)

 
"The corresponding sequence in OEIS is not a sequence that counts vowels. "

I guess that's the trouble, as its title purports to be:

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.

One needs to go to a comment to see the "trouble"

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


As far as this puzzle is concerned, one may or may not go with the way this OEIS sequence goes.







  Posted by Charlie on 2025-04-15 10:57:23
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