Definitions  natural numbers 
Let be n the sequence of natural numbers (A000027 on the OEIS), we define : 

the jump of n by (A000012) 
d(n) = 1 ; 

l(n) by 
l(n) = largest l such that 1 = n mod l, 0 if no such l exists, or 
l(n) = n  1 if n  1 > 1, 0 otherwise ; 

the weight by (A020639) 
k(n) = smallest k such that 1 = n mod k, 0 if no such k exists, or 
k(n) = smallest k greater than 1, that divides n  1 if n > 2, 0 otherwise ; 

the level by (A032742) 
L(n) = (n  1) / k(n) if n > 2, 0 otherwise. 

The weight is the smallest prime factor of n  1 and the level is the largest proper divisor of n  1. 
We have n = k(n) * L(n) + 1 (A000027(n) = A020639(n1) * A032742(n1) + 1) when n > 2. 

Principles of classification : For n <= 2, n is not classified. If for n, k(n) > L(n) then n is classified by level if not n is classified by weight. 
