The nth Pisano period, written π(n), is the period with which the sequence of Fibonacci numbers, modulo n, repeats. For example, the Fibonacci numbers mod 3 are 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, etc., with the first eight numbers repeating, so π(3)=8.
The first Pisano periods (sequence A001175 in OEIS) for n=1, 2, ... are:
- 1, 3, 8, 6, 20, 24, 16, 12, 24, 60, 10, 24, 28, 48, 40, 24, 36, 24, 18, 60, 16, 30, 48, 24, 100 ...
Pisano periods are named after Leonardo Pisano, better known as Fibonacci.
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