The Lucas Sequence is defined by recursion, and the initial seeds are
2 and 1. Your job is to design a program that will be able to detect if
a sequence of numbers is a part of the Lucas Sequence.
The Lucas Sequence
L1 = 2
L2 = 1
Ln = Ln-1 + Ln-2
(Each element of the sequence is the sum of the previous
two elements, except for L1 and L2.)
Input Format
The numbers in question will be listed in order one number per line.
There will be no more than five (5) numbers in each sample.
A -1 will signal the end of one test sequence.
A double -1 will be signal the end of the page.
The input file will be called jin02.txt.
Output Format
The results of the comparison.
The string "This is part of the Lucas Sequence." will be written if
it is part of the sequence.
The string "This is not part of the Lucas Sequence." if it is not a
part of the sequence.
Example Input
1
3
4
-1
150
456
606
1060
-1
-1
Output
This is part of the Lucas Sequence.
This is not part of the Lucas Sequence.