Problem 59741. Pivot index

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Let L be a vector of numbers. We are searching for the index n of the pivot element defined as follows: the dot product of the elements in the sub-vector to the left by their distance to the pivot element is equal to the dot product of the elements in the sub-vector to the right by their distance to the pivot element. 
Example 1: 
If L = [6,1,10,5,4], then n = 3 since :
Left sub-vector: L(1:n-1) = [6,1] and distances = [2,1] so dot product = 
Right sub-vector: L(n+1:end) = [5,4] and distances = [1,2] so dot product =  
Example 2:
If L = [10,3,3,2,1], then n = 2 since :
Left sub-vector: L(1:n-1) = [10] and distances = [1] so dot product = 
Right sub-vector: L(n+1:end) = [3,2,1] and distances = [1,2,3] so dot product =  