perplexus.info :: Sequences : Troublemaking Sequence

Troublemaking Sequence (Posted on 2025-04-15)

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, __

Submitted by Larry

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Solution: (Hide)

The n+1 term is the n-th term plus the number of vowels in the n-th term.
Depending on whether you consider 'y' a vowel or not, the next term is either 24 or 25.
A321676 in oeis is this sequence where 'y' is not considered to be a vowel.
The hint word Troublemaking in the title contains each vowel exactly once (but not y).
So, given that the word "Troublemaking" does not contain a 'y', there is some suggestion that only {a,e,i,o,u} should be counted and not 'y'; but a solution based on some other interpretation of what makes a vowel cannot be considered incorrect.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: Resolution in the formula	Charlie	2025-04-15 10:57:23
Resolution in the formula	Jer	2025-04-15 10:45:08
re: More trouble than you bargained for... (spoiler)	Larry	2025-04-15 09:56:02
More trouble than you bargained for... (spoiler)	Charlie	2025-04-15 08:54:02

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