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First, a story about how I messed up a puzzle:

It’s hard to make a simple yet creative number puzzle. After fiddling one late, dark winter evening with different patterns, at last I made a sequence of increasing numbers that I believed to be the smartest one ever.
Of course, I missed a little detail, as I do practically always when making puzzles at night so late, at 11:12. The sequence had been part of the OEIS!
Later, somebody searched OEIS, which gave the intended answer to the puzzle. Why does OEIS even contain such sequences? It isn’t even a mathematical progression! It is just a puzzle!
I have to take revenge. Should I find an unbelievably basic sequence which should be in the encyclopedia but isn’t? No, better yet, I’m finding some nice, random numbers that are in OEIS that you won’t get no matter what you search for!
They’re entirely, absolutely the products arising from my simple imagination. They can be discovered by looking at the clue hidden in plain view, and adding it at the location indicated by an isolated bunch of numbers. Good luck!

Now, find the pattern in this sequence:

3 6 8 11 13 14 22 25 27 35 37 45 60 80

*This is just a title. I do not hate OEIS. It's a good site.
OEIS stands for Online Encyclopedia of Integer Sequences, by the way.

Hint

I was surprised to see that some people counted the number of letters in words and yet missed an important clue...

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    $\begingroup$ The first 5 terms match these 18 sequences (but not the 6th term): oeis.org/search?q=3%2c6%2c8%2c11%2c13 $\endgroup$
    – boboquack
    Jan 13, 2018 at 5:00
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    $\begingroup$ @boboquack 1. Most 5-term increasing "reasonable" sequences match OEIS :) 2. "encyclopedia", thank you. $\endgroup$
    – Reinis Mazeiks
    Jan 13, 2018 at 5:11
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    $\begingroup$ I'd say 1, 3, 9, 10, 12 was pretty reasonable :P (second attempt) oeis.org/… $\endgroup$
    – boboquack
    Jan 13, 2018 at 5:54
  • $\begingroup$ @boboquack oh, I don't know how that happened. I tried about 6 sequences and they all matched. :) $\endgroup$
    – Reinis Mazeiks
    Jan 13, 2018 at 16:07
  • $\begingroup$ Does this sequence actually begin at 3? Not 1? $\endgroup$
    – Dr t
    Jan 14, 2018 at 22:13

1 Answer 1

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Partial solution

I believe that

the "isolated bunch of numbers" are 11:12 in the text portion.

My first guess as to the clue hidden in plain sight was

The phrase "the products arising from my simple imagination" - the word 'products' being a play on words and indicating numbers being multiplied together.

EDIT: I think I've spotted a couple major clues.

The products "arise from" my simple imagination, words with lengths 2, 6, and 11. Multiplying these together yields 132. So I'm guessing that's the clue, or part of it. Interesting that it's the same as eleven times twelve, the only two numbers given in the text.

Another discovery:

After poring over and analyzing the text for many different ciphers and acrostic hidden messages via obvious or well known steganography, the only remotely intelligible message or pattern that resulted was taking word n of paragraph n (word 1 of paragraph 1, word 2 of paragraph 2, etc.) and the result was: IT'S COURSE SEARCHED TAKE PRODUCTS. As Jay pointed out, this reinforces the "products" concept from earlier. Jay also discovered that the word lengths of the first part match the first three numbers in the sequence: 3 6 8. If you take the products of these, you obtain 144. Comparing this with the 132 from earlier, and we've got a couple multiples of twelve on our hands.

Per the latest hint:

Despite studying the word lengths before, I did notice after R.M prodded more in this direction, a pattern of repeating word lengths. It's still not crystal clear how to use it. Maybe someone else can spot it, or maybe I only have it partially. The pattern is:

6 6 4 4 2 2 6 6 4 4 8 8 4 4 4 4 11 11 2 2 2 2 4 4 4 4 2 2 2 2 4 4

Taken as a single pattern (assuming the doubles serve only to point out the correct sequence), it would be:

6 4 2 6 4 8 4 4 11 2 2 4 4 2 2 4

For completion's sake, assuming I've transcribed it correctly, the entire word length sequence is as follows, broken up by paragraphs.

3 4 2 4 1 6 3 8 6 6 5 8 3 4 4 6 7 4 9 8 2 4 1 4 1 8 2 10 7 4 1 8 2 2 3 8 3 4
2 6 1 6 1 6 6 2 1 2 11 6 4 6 7 2 5 2 4 2 3 8 3 4 4 2 3 4
5 8 8 4 5 4 3 8 6 2 3 6 3 4 4 4 7 4 9 2 4 4 1 11 11 2 2 4 1 6
1 4 2 4 7 6 1 4 2 11 5 8 5 6 2 2 3 12 3 4 2 6 3 2 7 4 4 6 7 4 3 2 4 4 3 4 3 2 6 4 3 6 3
6 8 10 3 8 7 4 2 6 11 4 3 2 10 2 7 2 3 4 6 2 5 4 3 6 2 2 3 8 9 2 2 8 5 2 7 4 4

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    $\begingroup$ The first sentence in each spoiler tag is on the right track. And there's something else that tells me that you're close to discovering an important hint... :) $\endgroup$
    – Reinis Mazeiks
    Feb 13, 2018 at 22:16
  • $\begingroup$ I'm awarding the bounty but there are a lot of loose ends in this answer. It's interesting to find the number 132 but it's not clear how this relates to the puzzle yet. Also @R.M has already disproved the connection to 14. I'm not sure how products will fit in, because there are so many primes in the sequence. You have actually edited out the part with 1st 2nd etc. words of each paragraph, which might have been the most important clue that has been found. $\endgroup$
    – Jay
    Feb 21, 2018 at 4:27
  • $\begingroup$ @Jay Thanks. I’ll have to take a look at what I edited out. I don’t remember any meaningful phrase that resulted which was any more convincing or concrete than what I’ve got here. As you said, it appears there’s a lot of work left to do. I’ve kept looking and plan to continue. $\endgroup$
    – Tim
    Feb 21, 2018 at 5:31
  • $\begingroup$ Yes, I'll keep looking too. The phrase seemed a little broken, but it reaffirmed the 'products' angle. I would not be surprised if there were other clues hidden in a similar way. $\endgroup$
    – Jay
    Feb 21, 2018 at 6:14
  • $\begingroup$ Hm... (rot13) Vgf pbhefr frnepurq = guerr fvk rvtug? $\endgroup$
    – Jay
    Feb 22, 2018 at 4:14

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