A131597 Bigomega of Pisano periods mod n, i.e., number of prime divisors (counted with multiplicity) of the period of Fibonacci residues mod n.

0, 1, 3, 2, 3, 4, 4, 3, 4, 4, 2, 4, 3, 5, 4, 4, 4, 4, 3, 4, 4, 3, 5, 4, 4, 4, 5, 5, 2, 5, 3, 5, 4, 4, 5, 4, 3, 3, 4, 4, 4, 5, 4, 3, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 3, 5, 5, 3, 2, 5, 4, 3, 5, 6, 4, 5, 4, 4, 5, 6, 3, 4, 3, 4, 5, 3, 5, 5, 3, 5, 6, 5, 5, 5, 5, 5, 4, 4, 3, 5, 5, 5, 5, 6, 5, 5, 4, 6, 5, 5, 3, 5, 5, 4, 5

Offset

1,3

Comments

The Pisano sequence (A001175) is not known exactly for all n. It is known that Pisano(n) <= 6n, Pisano(10) = 60, etc. (see A001175). In addition, Pisano(m) is even if m > 2, and Pisano(m) = m iff m = 24*5^(k-1) for some integer k > 1. Bigomega seems an interesting function of Pisano(n).

Links

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Pisano period.

Wikipedia, Pisano period.

Formula

a(n) = A001222(A001175(n)).

Example

F(mod 5): 0 1 1 2 3 0 3 3 1 4 0 4 4 3 2 0 2 2 4 1 0 1 1 ...
period = 20; bigomega = 3 (since 20 = 2*2*5).

Crossrefs

Cf. A000045, A001175, A001222.

Sequence in context: A094365 A272886 A098822 * A077070 A075988 A029150

Adjacent sequences: A131594 A131595 A131596 * A131598 A131599 A131600

Keyword

easy,nonn

Author

Paul Finley (pfinley(AT)touro.edu), Aug 30 2007

Status

approved