[math-fun] Digit-Fibonacci

I guess this is old hat (at least for the Fibonacci Quarterly); What could be the longest repeated pattern in a sequence where we just add the last two digits to produce the next term? Starting with 0,1, produces: 0,1,1,2,3,5,8,13,4,7,11,2,3,5,8,13,4,7,11,... where the repeated pattern is = [2,3,5,8,13,4,7,11] This pattern is 8-term long (or 10-digit long). Could one find a longest pattern with another start? Best, É.