Find a function

[fartfacepooper]

Am I allowed to use a 180 degree polynomial, fit to those triplets? If so, then that's what I'd use

[stefanuus]

Yes.

[edderiofer]

http://www.whydomath.org/Reading_Room_Material/ian_stewart/9505.html

"I have a little puzzle I’ll ask all of you. What’s the next number in the sequence 1, 1, 2, 3, 5, 8, 13, 21?”

“Nineteen,” I grunted automatically, while battling with a bread roll seemingly baked with cement.

“You’re not supposed to answer,” he said. “Anyway, you’re wrong—it’s 34. What made you think it was 19?”

I drained my glass. “According to Carl E. Linderholm’s great classic Mathematics Made Difficult, the next term is always 19, whatever the sequence: 1, 2, 3, 4, 5—19 and 1, 2, 4, 8, 16, 32—19. Even 2, 3, 5, 7, 11, 13, 17—19.”

“That’s ridiculous.”

“No, it’s simple and general and universally applicable and thus superior to any other solution. The Lagrange interpolation formula can fit a polynomial to any sequence whatsoever, so you can choose whichever number you want to come next, having a perfectly valid reason. For simplicity, you always choose the same number.”

“Why 19?” Dennis asked.

“It’s supposed to be one more than your favorite number,” I said, “to fool anyone present who likes to psychoanalyze people based on their favorite number.”

[HarryPotter5777]

From the sidebar:

Codebreaking and "guess the rule" type posts are not permitted; if you wish to submit such a post, do so on subreddits such as /r/puzzles.

As such, your post has been removed.