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16, ?, 19, ?, ?, 15, 16, 9, ?, ?, 14, ?, ?, ?, ?, 1

According to my measure, this sequence is more original than that of Fibonacci.

Replace the question marks with the missing numbers.

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  • $\begingroup$ I see 16 terms. Starts with 16 ends with 1. I also notice 9 is placed in correct numerical order if you count from 1-16. All three are square numbers in correct numerical order(from 1-16, that is). Am I on the right track or is it coincidental? $\endgroup$ – Prim3numbah Nov 25 '19 at 15:51
  • $\begingroup$ @Prim3numbah absolutely true what you say, also it is absolutely coincidental and you are absolutely on the wrong track. Minor hint: notice: one tag is not mathematics/or number sequence, but only "sequence". And also consider the other tags, they are all important. $\endgroup$ – user63710 Nov 25 '19 at 15:58
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Perhaps the sequence goes like this

16, 9, 19, 1, 14, 15, 16, 9, 19, 1, 14, 15, 16, 9, 19, 1, 14, 15, ...

being

the A1Z26 translation of "PISANO" repeated over and over. (Fibonacci, mentioned for no other obvious reason in the question, would originally have been called Leonardo Pisano; "Fibonacci" was a nickname.)

I confess that I don't know

why "measure" is italicized in the question if this is the intended answer.

Further remarks:

OP indicates in comments that the above is the right sequence but that I haven't understood exactly why it's the right sequence. Perhaps some other association of the name "Pisano" is relevant. A now-deleted comment from OP said something like "Measure = modulus", which to me is rather a stretch, but it suggests that perhaps OP had in mind the "Pisano periods", named after Leonardo Pisano = Fibonacci; this is the sequence of periods with which the Fibonacci sequence mod n repeats. (So e.g. the 7th Pisano period turns out to be 16 because when you do the Fibonacci thing mod 7 you get a repeating sequence of length 16.) But if this is what's intended then (1) the measure/modulus thing seems like a big stretch because the only context in which they mean at all the same thing is quite different and (2) I don't understand why "original" is italicized. There are some architects called Pisano (possibly including the person who designed the famous Leaning Tower), and it's in architecture that "measure" and "modulus" have related meanings, but again I don't then see what the italics on "original" are for. There are some other Pisanos but none that seems more obviously the intended one.

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  • $\begingroup$ Funnily enough, it seems you guessed the correct answer from an overly strong hint without getting the concept (and it was suspicious to you, too:), but I couldn't resist giving a green tick to the first lifeform ever to solve a puzzle of mine! :) $\endgroup$ – user63710 Dec 10 '19 at 11:11
  • $\begingroup$ Perhaps I still haven't "got the concept". Would you like to explain further? $\endgroup$ – Gareth McCaughan Dec 10 '19 at 12:00
  • $\begingroup$ No, would You like to solve it, or should this question remain open, awaiting the correct reasoning? $\endgroup$ – user63710 Dec 10 '19 at 12:03
  • $\begingroup$ Well, the question just asked what should replace the question marks, and apparently I got that right, so I maintain that I did solve it :-). I'll edit some more thoughts into my answer, but if they don't get to what you're driving at then perhaps more hints are needed. $\endgroup$ – Gareth McCaughan Dec 10 '19 at 12:21
  • $\begingroup$ This answer became a bit chaotic. In the "further remark" section there are a lot of irrelevancies now. Since it is not a mathematical sequence, "my modulus" doesn't need to be equal to 6 (the 6 different letters), nor the period= 24. You shouldn't have included so many subjective feelings about the puzzle when answering it. You also somehow brought back my comment which helped you to realize why "measure" was italicized (moderator thing), still, you left the part "I confess I don't know why italicized" in the answer. This became a big mess now. $\endgroup$ – user63710 Dec 10 '19 at 12:59

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