'Predict' the next few (5 or 6) terms of this series.
1, 1, 1, 2, 3, 6, 7, 10, 11, 12, 17, ...?
Hint: Who is the 'prime' suspect in this mystery sequence?
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$\begingroup$ This should be closed as "too broad" per puzzling.meta.stackexchange.com/a/5720/34791 $\endgroup$– Joseph Sible-Reinstate MonicaCommented May 25, 2019 at 16:30
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$\begingroup$ Also, don't edit puzzles after they're posted. You invalidated my answer for no legitimate reason. $\endgroup$– Joseph Sible-Reinstate MonicaCommented May 25, 2019 at 16:31
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1$\begingroup$ I did so because then it would look the same as sequence you mentioned and invite further similar thoughts. There was no bad intention. $\endgroup$– Mike KarterCommented May 25, 2019 at 16:32
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2 Answers
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14, 17, 27, 34, 55, 63. This is just OEIS A000837: Number of partitions of n into relatively prime parts.
Note: This answer was written when only the terms "1,1,1,2,3,6,7" were in the puzzle. The OP added more terms to the puzzle after this answer was written.
answered May 25, 2019 at 16:09
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1$\begingroup$ That was not the intention. However, thank you for the answer. Can you think of something else ? $\endgroup$ Commented May 25, 2019 at 16:22
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3$\begingroup$ I do not agree that OP added more terms to make this "wrong". Rather, he added more terms to clarify the problem. This does not necessarily change the answer they had in mind. Never assume malice over err. $\endgroup$ Commented May 25, 2019 at 19:48
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1$\begingroup$ Putting it another way: (1) Presumably the OP has some other answer in mind (i.e., other than the answer you posted). (2) Since the edit extended the sequence, but didn’t change any numbers that were already posted, it follows that the OP’s intended answer was an answer to the original version of the question. (3) Your answer satisfied the original version of the question. Therefore, by definition, the original version of the question had multiple correct(ish) answers. If a question has multiple correct answers, we call it “too broad”. … (Cont’d) $\endgroup$ Commented May 25, 2019 at 22:23
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1$\begingroup$ (Cont’d) … (4) When a question is too broad, the author is encouraged to edit it to narrow the scope; i.e., to rule out answer(s) other than the intended one. This happens all the time. It’s tough luck to stumble across a question that’s too broad, provide an answer that’s correct, and then be told that it’s not what the OP meant / wanted, but it happens all the time. Please do not accuse the OP of singling you out or attacking you ‘‘for no legitimate reason’’. $\endgroup$ Commented May 25, 2019 at 22:23
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$\begingroup$ @PeregrineRook Fair; answer edited. $\endgroup$ Commented May 25, 2019 at 22:35
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WARNING this answer is probably very wrong.
I am bad at wording things so I put a visual. It's like pascal's triangle but with subtraction.
The second line of the blue pascal's triangle shows
0, 0, 1, 1, 3, 1, 3, 1, 1, 5
Which may be a fractal-like series. Again i'll show you it, not knowing how to explain it:
0
0
1
1, 3, {1}, 3, 1
1, 5, {1, 3, 1, 3, 1}, 5, 1
1, 7, {1, 5, 1, 3, 1, 3, 1, 5, 1}, 7, 1
And somehow the zeroes get added back in after the infinite series.
So therefore the pattern of differences will be
0, 0, 1, 1, 3, 1, 3, 1, 1, 5, 1, 3, 1, 3, 1, 5, 1, 1, 7 etc.
And finally, by adding the differences back into the numbers, we get:
1, 1, 1, 2, 3, 6, 7, 10, 11, 12, 17, 18, 21, 22, 25, 26, 31, 32, 33, 40 etc.
YAYYY!!!!
