As you probably know, a Fibonacci Number is one which is the sum of the previous two numbers in the series.
A Fibonacci Digit™ is one which is the sum of the two previous digits.
For instance, for the series beginning
1,1, the series would be
1,1,2,3,5,8,13,4,7,11,2... The change occurs after the
13, where, instead of adding
8+13, you add
1+3. The series loops at the end, where
1+1=2, same as the series starts.
For another example, the series beginning
2,2,4,6,10,1,1,2,3,5,8,13,4,7,11,2,3.... This one starts out uniquely, but once the digits sum to
10, you end up with
1+0=1, 0+1=1, and the series continues - and loops - the same way the
1,1 series did.
Given an integer input
0≤n≤99, calculate the loop in the Fibonacci Digit series beginning with those two digits. (You are certainly allowed to consider integers out of this range, but it's not required.) If given a one-digit input, your code should interpret it to denote the series beginning
All numbers in the loop that are two-digits must be outputted as two digits. So, for instance, the loop for
1,1 would contain
The output begins with the first number in the loop. So, based on the above restrictions, the loop for
1,1 begins with
11 are counted separately.
Each number of the output may be separated by whatever you want, as long as it's consistent. In all of my examples I use commas, but spaces, line breaks, random letters, etc. are all allowed, as long as you always use the same separation. So
2g3g5g8g13g4g7g11 is a legal output for
2j3g5i8s13m4g7sk11 is not. You can use strings, lists, arrays, whatever, provided that you have the correct numbers in the correct order separated by a consistent separator. Bracketing the entire output is also allowed (ex.
1 -> 2,3,5,8,13,4,7,11 2 -> 2,3,5,8,13,4,7,11 3 -> 11,2,3,5,8,13,4,7 4 -> 3,5,8,13,4,7,11,2 5 -> 2,3,5,8,13,4,7,11 6 -> 3,5,8,13,4,7,11,2 7 -> 14,5,9 8 -> 13,4,7,11,2,3,5,8 9 -> 11,2,3,5,8,13,4,7 0 -> 0 14 -> 5,9,14 59 -> 5,9,14
This is code-golf, so the lowest number of bytes wins.