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


Hint : Autobots, This is Optimus Prime.

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    – Rubio
    Jul 20, 2019 at 5:51

1 Answer 1


I think that the next term is



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 $p_7 + q_7 = 17 + 16 = 33$

  • $\begingroup$ how does this fit with the hint? $\endgroup$
    – JMP
    Jun 3, 2019 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, 2019 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, 2019 at 19:59

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