# 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 throw 0 : 1 2 3 4 5 6 7 8 throw 1 : 2 3 1 4 5 6 7 8 throw 2 : 3 1 4 2 5 6 7 8 throw 3 : 1 3 4 2 5 6 7 8 throw 4 : 3 4 2 1 5 6 7 8 throw 5 : 4 2 1 5 3 6 7 8 

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?

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