A356550 a(n) is the period of {F(F(k)) mod n, k >= 0}, where F denotes the Fibonacci numbers (A000045).

1, 4, 12, 24, 60, 12, 24, 24, 24, 60, 60, 24, 48, 24, 60, 24, 24, 24, 24, 120, 24, 60, 24, 24, 300, 48, 24, 24, 48, 60, 120, 24, 60, 24, 120, 24, 18, 24, 48, 120, 60, 24, 60, 120, 120, 24, 48, 24, 48, 300, 24, 48, 72, 24, 60, 24, 24, 48, 42, 120, 120, 120, 24

Offset: 1

Author

Rémy Sigrist, Aug 11 2022

Keywords

• nonn

Comments

F(F(k)) mod n = F(F(k mod pi(pi(n))) mod pi(n)) mod n (where pi = A001175), so F(F(k)) mod n is periodic and the sequence is well defined.

Examples

			For n = 6:
- A001175(A001175(6)) = A001175(24) = 24,
- the values of F(F(k)) mod 6 for k = 0..23 are:
          0, 1, 1, 1, 2, 5, 3, 5, 2, 1, 1, 1, 0, 1, 1, 1, 2, 5, 3, 5, 2, 1, 1, 1
- we see that F(F(k)) mod 6 = F(F(k+12)) mod 6,
- so a(6) = 12.
		

Links

• Rémy Sigrist, PARI program

Crossrefs

Cf. A000045, A001175, A007570.

Programs

PARI

See Links section.

Formula

a(n) divides A001175(A001175(n)).