Combinatorics is, amongst others, about counting discrete structures. Factorial, used in Newton’s symbol, is big part of it. It is also directly connected to the primes – it is only about multiplication, and multiplication is used for counting elements (iteration of addition). And L-sequence is the next step to revise it. Every integer can be represented as . L-sequence is for factorials. Below the first values. **If you think about it, factorial is also the closest possible thing to Riemann’s Zeta function! **Connecting the Zeta function with the analysis of behavior of factorials might be crucial to understanding the distribution of primes.

From there on, I am creating the factorial triangle.

Tasks

1. Find the formula that describe row values in the triangle.

2. **Notice that in the column associated with -th prime, we have times 1, then times 2,.., would that be true in general?**

Now, look at places when “new” primes come into play:

And finally, at sequences –** how are those sequences related?**

1,2,3,4,5,6,7,.. (missing some prime)

1,1,2,2,3,3,4,4,5,5,…(missing some prime,prime)

1,1,1,2,2,2,3,3,3,4,4,4,…(missing some prime,prime,prime)

(1,1,..,1)(2,2..,2),..(missing some prime,…,prime)

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