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I have a homework. It seems to be an easy sequence but I can't get the answer. So, What is the next element? $$2, 7, 10, 13, 23, 34,?$$

What would be the solution out of these numbers? 45 or 49 or 58 or 39

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OEIS couldn't find any possible pattern. –  B. S. Jan 9 at 9:07
    
If I say that the solution must be out of these numbers, and there is only 1 correct, what would be the solution?: 45 or 49 or 58 or 39 –  Student Jan 9 at 9:28
    
see below: there is no "unique" solution: any of those is as good as any other –  Bernd Jan 9 at 9:32
    
see the discussion at math.stackexchange.com/questions/55952/… –  Andrea Mori Jan 9 at 11:15
    
I would continue with $10+13+23+4=50$. –  Phira Jan 9 at 17:26
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1 Answer

Those questions are most of the times "useless", meaning they don't have unique answers. Sometimes, you can see an obvious pattern (e.g. 2,4,8,16,32,...) which makes you think there is only one continuation (64,128). Sometimes there are more than one patterns (don't have an example right away - will think about one). From a mathematical point of view, any continuation is possible.

In your case, there isn't an obvious pattern. Maybe there is a hidden pattern (like modulo a certain prime, numbers for letters etc.), but it is not obvious. So any continuation is mathematically as good as the other.

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Examples of other continuations: oeis.org/A001592 and oeis.org/A006261 –  Daniel R Jan 9 at 9:29
    
@Daniel Thank you –  Bernd Jan 9 at 9:32
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