MathDB

The number

1

is written on the blackboard. After that a sequence of numbers is created as follows: at each step each number

a

on the blackboard is replaced by the numbers

a - 1

and

a + 1

; if the number

0

occurs, it is erased immediately; if a number occurs more than once, all its occurrences are left on the blackboard. Thus the blackboard will show

1

after

0

steps;

2

after

1

step;

1, 3

after

2

steps;

2, 2, 4

after

3

steps, and so on. How many numbers will there be on the blackboard after

n

steps?

Problem Statement