[seqfan] A Fibonacci-related sequence -- suggestion
Lars Blomberg
lars.blomberg at visit.se
Thu Jun 7 18:45:53 CEST 2012
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
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