MathDB

We are given an infinite sequence of

1

's and

2

's with the following properties: (1) The first element of the sequence is

1

. (2) There are no two consecutive

2

's or three consecutive

1

's. (3) If we replace consecutive

1

's by a single

2

, leave the single

1

's alone, and delete the original

2

's, then we recover the original sequence. How many

2

's are there among the first

n

elements of the sequence? P. P. Palfy

Problem Statement