[seqfan] A Fibonacci-related sequence -- suggestion

[Lars Blomberg]

Hello SeqFans,

a(n) is the cycle length of the first differences of numbers k satisfying

Fib(k) mod n = k mod n



Example with n=3:

Fib(k):

0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368

Fib(k) mod 3:

0,1,1,2,0,2,2,1,0,1,1,2,0,2,2,1,0,1,1,2,0,2,2,1,0

k mod 3:

0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0

accepted k values indicated by x:

x,x,-,-,-,x,-,x,-,-,x,x,x,-,-,-,-,-,-,-,-,-,-,-,x

accepted k values:

0,1,5,7,10,11,12,14,24

first differences of k values:

1,4,2,3,1,1,2,10

after this the cycle repeats, so a(3)=8.



Beginning of the sequence:

a(n)=3,8,3,8,6,16,3,8,14,10,4,28,24,16,3,36,6,18,11,16,15,48,3 for n=2..24



It is not in OEIS, should it be?



Regards,

LBg