$[3,6,11,18,27,38,...]$. I need to write this set in set-builder notation but I can't find any pattern, I see no common multiple, it doesn't appear to be a geometric or arithmetic series. The problem comes from the book of proof.
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6Look at their differences. – Sep 21 '17 at 17:00
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1http://oeis.org is your friend – Coolwater Sep 21 '17 at 17:00
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Given only six integers, it's quite a leap to find a pattern based on only six integers, to apply to countably infinitely many integers. Given the six integers you include, we have a difference of 3, 5, 7, 9, 11, ... – amWhy Sep 21 '17 at 17:03
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differences 3,5,7,9...... – Sep 21 '17 at 17:03
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1subtract $2$ from each term. – Angina Seng Sep 21 '17 at 17:05
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$$A={x\in\mathbb{N}|x=n^2 + 2,;\forall n\in\mathbb{N}\land n>0}$$ – Raffaele Sep 21 '17 at 17:07
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In general the answer to "what is the next number in this sequence" is "anything you want it to be", unless you put some constraint on the nature of the generating function. But $n^2+2$ is probably the simplest answer here. – Joffan Sep 21 '17 at 17:11
