When first 75T digits of Pi searched for sequence of “666666666666” (12 consequent 6s). In total there are 57 matches. And there is only one instance with additional following 6s. And it is a sequence of 17 6s. (15th match.)
…92827152450 666666666666 6666694778940… (Starts at location: 28642224609576. Not including “3.”)
(Can be checked from pi.delivery where I obtained digits.)
(Any specific sequence of 17 digits on average occurs once in every 100000 trillions digits. 13 digit occurs once in 10 trillion.)
oeis.org (This database also confirms there aren't any 12+ consequent 6s until 80+ Trillion.)
pi-e.de (I guess this is a database for first occurrences. Not sure.)