A213277 a(n) is the length of the cycle of first differences of k such that Fibonacci(k) mod n = k mod n.
3, 8, 3, 8, 6, 16, 3, 8, 14, 10, 4, 28, 24, 16, 3, 36, 6, 18, 11, 16, 15, 48, 3, 18, 42, 8, 12, 14, 14, 30, 3, 40, 18, 32, 4, 76, 9, 56, 11, 40, 12, 88, 15, 16, 24, 32, 3, 16, 34, 24, 21, 108, 6, 8, 6, 24, 21, 58, 12, 60, 15, 16, 3, 56, 30, 136, 9, 16, 56
Offset: 2
Keywords
Examples
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.
Links
- Lars Blomberg, Table of n, a(n) for n = 2..23002
Comments