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I know that "next number" questions are not popular here, but this one is tough and I couldn't figure out the pattern. To give an idea one of the questions had a pattern of $\operatorname{Prime}(\operatorname{Fib}(n))$.

So this is the series:

$$0, 0, 2, 6, 12, 21, 34, 51$$ What is the next number in the series ?

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    $\begingroup$ OEIS has nothing. Even when removing the initial $0$'s to account for possible different initial point. $\endgroup$ – Arthur Dec 5 '18 at 20:05
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    $\begingroup$ Could you give some context? Where did you see this question? $\endgroup$ – Kevin Long Dec 5 '18 at 20:07
  • $\begingroup$ My friend asked me this question, he said he saw it in a competition. $\endgroup$ – papabiceps Dec 5 '18 at 20:14
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    $\begingroup$ @papabiceps Ew, a "what's the next number" question in a competition? Yuck. $\endgroup$ – Franklin Pezzuti Dyer Dec 5 '18 at 21:02
  • $\begingroup$ The problem with "next number" questions is that unless a specific rule is given to generate the next number, it can be anything. That is why they are unpopular on Math.SE. +1 to Frpzzd's comment. $\endgroup$ – parsiad Sep 1 at 2:04
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I'll find some pattern and then claim a correct answer:

0, 0, 2, 6, 12, 21, 34, 51

0, 2, 4, 6, 9, 13, 17

2, 2, 2, 3, 4, 4

Then 4 + 17 = 21 and 21 + 51 = 72 .

Well, {2, 2, 2, 3, 4, 4} calls for {2, 2, 2, 3, 4, 4, 4} but a continuing pattern is debatable after that. It might be {2, 2, 2, 3, 4, 4, 4, 5, ...}.

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  • $\begingroup$ Can you elaborate? $\endgroup$ – johnnycrab Dec 5 '18 at 20:53
  • $\begingroup$ @johnnycrab Binomial transform. But not very convincing here. $\endgroup$ – Jean-Claude Arbaut Dec 5 '18 at 21:15
  • $\begingroup$ @Jean-Claude Arbaut Thanks, didn't see it from just looking at the numbers. $\endgroup$ – johnnycrab Dec 5 '18 at 21:18

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