ALGO: What is Catalan number and what types of problems can be solved by using Catalan number series/formula ?

Question

1,1,2,2,2,6,6,6,7,7,7,7,7,7,7,8,8,9,9,9

Example:
Input = 1 Output=0 (First index of 1).
Input = 2 Output=2 (First index of 2).
Input = 6 Output= 5 (First index of 6).
Input = 7 Output= 8 (First index of 7).
Input = 8 Output=15 (First index of 8).
Input = 9 Output=17 (First index of 9).