A356550 - OEIS

%I #5 Aug 15 2022 05:19:56

%S 1,4,12,24,60,12,24,24,24,60,60,24,48,24,60,24,24,24,24,120,24,60,24,

%T 24,300,48,24,24,48,60,120,24,60,24,120,24,18,24,48,120,60,24,60,120,

%U 120,24,48,24,48,300,24,48,72,24,60,24,24,48,42,120,120,120,24

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

%C 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.

%H Rémy Sigrist, <a href="/A356550/a356550.gp.txt">PARI program</a>

%F a(n) divides A001175(A001175(n)).

%e For n = 6:

%e - A001175(A001175(6)) = A001175(24) = 24,

%e - the values of F(F(k)) mod 6 for k = 0..23 are:

%e           0, 1, 1, 1, 2, 5, 3, 5, 2, 1, 1, 1, 0, 1, 1, 1, 2, 5, 3, 5, 2, 1, 1, 1

%e - we see that F(F(k)) mod 6 = F(F(k+12)) mod 6,

%e - so a(6) = 12.

%o (PARI) See Links section.

%Y Cf. A000045, A001175, A007570.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Aug 11 2022