3
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Find the next terms and also, explain the logic used for the terms of the sequence.

$3,7,11,15,20,27,?????$

Hint : Autobots, This is Optimus Prime.

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  • $\begingroup$ Has a correct answer been given? If so, please don't forget to $\color{green}{\checkmark \small\text{Accept}}$ it. (That indicates what the correct answer is, so there's no doubt; it also awards the successful answerer for their effort, and as an added bonus, gives you +2 rep for doing it! It's also just good etiquette for this site. You have a few questions right now that seem to have good answers, and none have been accepted; please consider doing so. Thanks!) $\endgroup$ – Rubio Jul 20 at 5:51
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I think that the next term is

$33$

Reasoning

Let $p_n$ be the sequence of prime numbers: $2,3,5,7,11,13,17, \ldots$
Let $q_n$ be the sequence of positive non-prime numbers composed solely of positive non-prime digits: $1,4,6,8,9,14,16,\ldots$

The $n$th term of the sequence above is $p_n + q_n$ which makes the $7$th term $p_7 + q_7 = 17 + 16 = 33$

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  • $\begingroup$ how does this fit with the hint? $\endgroup$ – JonMark Perry Jun 3 at 18:54
  • $\begingroup$ I think the hint is meant to refer to these oeis.org/A217090, you might want to see if that clarifies your solution at all. $\endgroup$ – JProblems Jun 3 at 18:58
  • $\begingroup$ @JonMarkPerry Really I just honed in on the word prime, not sure how autobots come into it. $\endgroup$ – hexomino Jun 3 at 19:59

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