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

1,2

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.

Links

Table of n, a(n) for n=1..63.

Rémy Sigrist, PARI program

Formula

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

Example

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.

Prog

(PARI) See Links section.

Crossrefs

Cf. A000045, A001175, A007570.

Sequence in context: A136486 A003203 A051193 * A216244 A215223 A318610

Adjacent sequences: A356547 A356548 A356549 * A356551 A356552 A356553

Keyword

nonn

Author

Rémy Sigrist, Aug 11 2022

Status

approved