ROSECODE 448

Best Matrices Multiplication 2

Min_25 · Math · 2017-11-21

Let $A$ be an infinite sequence of matrices $A := (A_{1}, A_{2}, \dots)$ .

$A_{i}$ has $x_{i}$ rows and $x_{i + 1}$ columns, where $x_{n} = 5000 + (r_{n} mod 1000)$ and $r_{1} = 2, r_{n} = r_{n - 1}^{2} mod 98765431 (n \geq 2) .$

Let $C (n)$ be the minimum cost of matrix multiplication of $A_{1}, \dots, A_{n}$ .

(see Problem 436 for the cost.)

For example, $x_{1} = 5002$ , $x_{11} = 5053$ , $C (3) = 257423728320$ and $C (10) = 1290936750576$ .

Find $C (6543)$ .