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Problem #448

Best Matrices Multiplication 2
 Public ★(x8) 11/21/17 by Min_25 9xp Math 100.0%

Let $A$ be an infinite sequence of matrices $A := (A_1, A_2, \ldots)$.

$A_i$ has $x_i$ rows and $x_{i+1}$ columns, where $$x_n = 5000 + (r_n \bmod 1000)$$ and $$r_1 = 2, r_n = r_{n-1}^2 \bmod{98765431}\ (n \ge 2).$$

Let $C(n)$ be the minimum cost of matrix multiplication of $A_1, \ldots, A_n$.

(see Problem 436 for the cost.)

For example, $x_1 = 5002$, $x_{11} = 5053$, $C(3) = 257423728320$ and $C(10) = 1290936750576$.

Find $C(6543)$.

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