# Another Number Sequence…Yayy!

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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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 $$p_7 + q_7 = 17 + 16 = 33$$

• how does this fit with the hint? – JMP Jun 3 '19 at 18:54
• 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. – JProblems Jun 3 '19 at 18:58
• @JonMarkPerry Really I just honed in on the word prime, not sure how autobots come into it. – hexomino Jun 3 '19 at 19:59