20 Questions Type Puzzel

[TheRealJoeFish]

To bookend, the "other" solution, other than 143, was 165.

2
2*2+2 = 6
6*6+3 = 15
15*2+5 = 35
35*2+7 = 77
77*2+11 = 165

and so on!

How does the first term fit the sequence in this case? There is no natural prime number before 2.

The first term being 2? You just have to define it. Each term in the sequence depends on the number before it, but the first term in the sequence by definition doesn't have a number before it. So you've just got to start somewhere.

For instance, the initial 1, 1 doesn't "fit" the Fibonacci sequence. That's just where you start.