Integer sequence
An integer sequence is a sequence (i.e. an infinite list) of integers.
An integer sequence may be specified explicitly by giving a formula for its n-th term, or implicitly by giving a relationship between its terms. For example, the sequence 1, 1, 2, 3, 5, 8, 13, ... (the Fibonacci sequence) is formed by starting with two ones and then adding any two consecutive terms to obtain the next one: an implicit description. The sequence 0, 3, 8, 15, ... is formed according to the formula n2 - 1 for the n-th term: an explicit definition.

1/1 = 1.0000
1/2 = 0.5000
2/3 = 0.6667
3/5 = 0.6000
5/8 = 0.6250
8/13 = 0.6154
13/21 = 0.6190
21/34 = 0.6176
34/55 = 0.6182
55/89 = 0.6180
89/144 = 0.6181
144/233 = 0.6180
233/377 = 0.6180


As we go further and further along the sequence of Fibonacci fractions, their decimal
digits settle down. If we kept track of twenty decimal digits, and went out a lot
further out in the sequence, we would find that
the number settles down to 0.61803398874989484820.
What is this number 0.61803...?
It is one of the most amazing numbers in the universe. We can see it in the
mystical pentagram which we construct by taking five equally spaced points around a circle
and joining them in all possible ways