Developments 

Since we know that the weight of n is the smallest prime factor of n  1 and that the level is the largest proper divisor of n  1 ,
the decomposition into weight * level + jump is a reformulation of the sieve of Eratosthenes and we have the following relations : 
L(n) = 1 <=> k(n) > L(n) <=> k(n) = l(n) = n  1 <=> l(n) = n  1 is prime 
L(n) > 1 <=> k(n) <= L(n) <=> k(n) * L(n) = l(n) = n  1 <=> l(n) = n  1 is composite 
If n is classified by level (or if n is of level 1) then n  1 is prime and if n is classified by weight, n  1 is composite. 


