ROSECODE 281

Awesome algorithm

Philippe_57721 · Math · 2015-11-28

Given a vector

A

of rational numbers, we define the following transformation :

B = {1 \times (A_{1} - A_{2}), 2 \times (A_{2} - A_{3}), 3 \times (A_{3} - A_{4}), \dots}

We repeat the process:

C = {1 \times (B_{1} - B_{2}), 2 \times (B_{2} - B_{3}), 3 \times (B_{3} - B_{4}), \dots}

And so on ...

Consider now the vector

Z = {B_{1}, C_{1}, D_{1}, \dots}

A = {\frac{1}{1}, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \dots}

, find the first index

i

for which the denominator of

Z_{i}

is greater than

10^{50}

.
Answer format: index,denominator
[My timing: < 1 sec]