In the English Premier League both Blackburn Rovers and Leicester City have won one title, Liverpool has won two titles, Arsenal has won three titles, Chelsea has won five titles, Manchester City has won eight titles and Manchester United has won 13 titles.
The number of wins by these seven teams (1, 1, 2, 3, 5, 8, 13) form a Fibonacci sequence.
Clearly this sequence will be broken no matter which team wins this season.
But it is possible, some time in the future, that the number of wins by the teams that win the Premier League could, once again, form a Fibonacci sequence. What is the fewest number of seasons before this is possible, although it is rather unlikely?
Note: this is the standard Fibonacci sequence starting 1, 1 or 0, 1, 1.
The sum of the first seven values in the Fibonacci sequence (1 + 1 + 2 + 3 + 5 + 8 + 13) is 33.
The next value after 13 is (8 + 13) 21, so the sum of the first eight values is (33 + 21) 54.
So in 21 seasons time it is possible for another Fibonacci sequence to form.
This is clearly the case if some new, dominant team won the next 21 Premier League titles. It would also be possible if one other team wins some titles and the seven existing winners win the correct amounts to make the sequence.
But it will take exactly 21 seasons, IF it happens.