2,7,15,33.........................................

Question

What is the next two numbers in the sequence

Answer 1

2, 7, 15, 33, 

3, 8, 16, 34, (add 1) ---- t_n+1

6, 16, 32, 68, (double) ---- 2(t_n+1)

6+1=7, 16-1=15, 32+1=33,  (alternately add or subtract 1) ---- 2(t_n+1)+(-1)ⁿ

So the next two terms in the sequence are 67 and 137.

Rule is: t_n+1=2(t_n+1)+(-1)ⁿ where t₀=2; t₁=2(2+1)+1=7; t₂=2(7+1)-1=15; t₃=2(15+1)+1=33; t₄=2(33+1)-1=67; t₅=2(67+1)+1=137.