A177824 - OEIS

%I #10 Apr 26 2020 23:15:23

%S 0,0,6,5,1,6,2,1,0,0,6,5,1,6,2,1,0,0,6,5,1,6,2,1,0,0,6,5,1,6,2,1,0,0,

%T 6,5,1,6,2,1,0,0,6,5,1,6,2,1,0,0,6,5,1,6,2,1,0,0,6,5,1,6,2,1,0,0,6,5,

%U 1,6,2,1,0,0,6,5,1,6,2,1,0,0,6,5,1,6,2,1,0,0,6,5,1,6,2,1

%N a(n) = (Fibonacci(n)*Fibonacci(n+7)) mod 7.

%C The function f(k,n) = (Fibonacci(n)*Fibonacci(n+k)) mod k appears to be periodic. The repeated values for successive values of k are

%C k=2...[0,0,1]

%C k=3...[0,2,1,0]

%C k=4...[0,1,0,2,3,2]

%C k=5...[3,3,2,2,0,2,2,3,3,0]

%C k=6...[0,1,3,2,3,1,0,5,3,4,3,5]

%C k=7...[0,0,6,5,1,6,2,1]

%C k=8...[0,2,7,2,0,5]

%C k=9...[0,1,8,0,6,4,2,6,3,7,5,3]

%C k=10..[0,9,4,6,1,0,6,1,4,4,5,4,4,1,6,0,1,6,4,9,0,4,9,6,6,5,6,6,9,4]

%C Periodicity of 8.

%p with(combinat):

%p seq((fibonacci(n)*fibonacci(n+7)) mod 7, n=0..50);

%t Table[Mod[Fibonacci[n]Fibonacci[n+7],7],{n,0,100}] (* _Harvey P. Dale_, Oct 01 2017 *)

%K nonn

%O 0,3

%A _Gary Detlefs_, Dec 13 2010