Tougher Throwing Numbers
Consider the sequence of positive integers \(1,2,3,4,5,6, \ldots \). An operation throw
consists of taking the first number and move it to the back of the \((k+1)^\text{th}\) number where \(k\) is the second number in the sequence. For example,
1 2 3 4 5 6 

The first occurrence of 2, 3, 4, 5 being the head of the sequence are after 1, 2, 5 and 12 throws, respectively. How many throw
operations do you need to perform to get 20 in the head of the sequence?