1,2,3,3,6,5,10,8,15,13

The given sequence alternates between two distinct patterns:

1. Triangular Numbers: At odd positions (1st, 3rd, 5th, 7th, 9th):

( 1, 3, 6, 10, 15 )

These follow the formula ( frac{n(n+1)}{2} ), where ( n ) starts at 1 and increments by 1 each step. The next term is ( 21 ) (since ( frac{6 cdot 7}{2} = 21 )).

2. Fibonacci-like Sequence: At even positions (2nd, 4th, 6th, 8th, 10th):

( 2, 3, 5, 8, 13 )

Each term is the sum of the two preceding terms. The next term is ( 21 ) (since ( 8 + 13 = 21 )).

Next Terms:

The sequence continues as ( 21 ) (11th term, triangular) followed by ( 21 ) (12th term, Fibonacci). Thus, the next two terms are:

[

boxed{21, 21}

]