A Lucas chain for an integer 
is an increasing sequence
 |
of integers such that every 
,
, can be written as a sum 
of smaller elements whose
difference 
is also en element of the sequence or zero (i.e., taking 
is allowed). The number 
is called the length of the chain.
For example, 
is a Lucas chain of length 3 for 5 because 
, 
, 
, 
, 
, and 
. Further examples are sequences of consecutive powers
of 2 or the Fibonacci numbers 1, 2, 3, 5, 8,
13, 21, ....
Lucas chains are a special kind of addition chain and can be used to evaluate Lucas functions, which have been proposed for use in public-key cryptography.
via Lucas Chains." Unpublished manuscript.