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Find the next number in this sequence:

2, 4, 6, 9, 14, 18, 25, 32, 44, ?

Bonus question: I originally was going to use a different related sequence which grew at a faster rate, but changed it to this one instead. What was the original sequence, and why might I have opted for this one instead?

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1 Answer 1

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The next number is

63

The sequence seems to be

$a_n = F_n + P_n$, the $n$-th Fibonacci number plus the $n$-th prime number

0+2, 1+3, 1+5, 2+7, 3+11, 5+13, 8+17, 13+19, 21+23, so the next number is 34+29

And my guess for bonus,

perhaps you originally multiplied, but didn't like that because it'd have been more obvious if we'd factored the numbers

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    $\begingroup$ Correct on all accounts. That was exactly my reasoning for the bonus question. $\endgroup$
    – TTT
    Feb 1, 2016 at 22:15

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