Looking at the Fibonacci sequence but, specifically their moduli.

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Lengths: 3, 8, 6, 20, 24

Fib mod(2)

1,1,0….

Fib mod(3)

1, 1, 2, 0, 2, 2, 1, 0…

Fib mod(4)

1, 1, 2, 3, 1, 0…

Fib mod(5)

1, 1, 2, 3, 0, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0, 2, 2, 4, 1, 0…

Fib mod(6)

1, 1, 2, 3, 5, 2, 1, 3, 4, 1, 5, 0, 5, 5, 4, 3, 1, 4, 5, 3, 2, 5, 1, 0…