lorb wrote:It seems you are looking for a closed formula for this?

Exactly!

But I want to reach it using other sequence easy to find.

I still do not know how to simplify the second sequence the negative.

All the results will be the first step to have another formula for the prime counting function.

To compute the numbers of prime up to n is not easy.

I know that I`m using a list of primes that is obvious.

I`m not fool.