A mathematical number sequence

Can you deduce the next three terms and long term behaviour?

$$0, 1, 1, 2, 3, 7, 22, 29, 45, 100, \dots$$

This sequence is not in the Online Encyclopedia of Integer Sequences (OEIS).

The sums of the digits of each to consecutive numbers are multiplied and then to the product 1 is added For example: 0 x 1 + 1 = 1
1 x 1 + 1 = 2
...
3 x 7 + 1 = 22
7 x 4 + 1 = 29 (2 + 2 = 4)
therefore:
9 x 1 + 1 = 10
1 x 1 + 1 = 2
1 x 2 + 1 = 3

so, the next 3 numbers are 10, 2, 3

• Yes, good job, well done :-) – tom Apr 8 '18 at 13:09