Definitions 
Let be a(n) an integer sequence strictly increasing, we define : 

the jump of a(n) by 
d(n) = a(n+1)  a(n) ; 

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

the weight by 
k(n) = smallest k such that d(n) = a(n) mod k, 0 if no such k exists, or 
k(n) = smallest k greater than d(n), that divides l(n), 0 if l(n)=0 ; 

The level by 
L(n) = l(n) / k(n), 0 if k(n) = 0. 

The weight k(n) is the smallest such that in in the Euclidean division of a(n) by its weight k(n), the quotient is the level L(n), and the remainder is the jump d(n). 
We have a(n) = k(n) * L(n) + d(n) = weight * level + jump when l(n) is different from 0 which can be rewritten when a(n+1) < (3/2) * a(n). 

Principles of classification : if for a(n), l(n) = k(n) = L(n) = 0 then a(n) is not classified. If for a(n), k(n) > L(n) then a(n) is classified by level , if not then it is classified by weight. 
