A093089 "Fibonacci in pairs": start with a(1)=1, a(2)=1; repeatedly adjoin sum of previous two terms but chopped from the right into pairs of 2 digits.

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 1, 44, 90, 45, 1, 34, 1, 35, 46, 35, 35, 36, 81, 81, 70, 71, 1, 17, 1, 62, 1, 51, 1, 41, 72, 18, 18, 63, 63, 52, 52, 42, 1, 13, 90, 36, 81, 1, 26, 1, 15, 1, 4, 94, 43, 14, 1, 3, 1, 26, 1, 17, 82, 27, 27, 16, 16, 5, 98, 1, 37, 57, 15, 4, 4, 27, 27, 18