A093088 "Fibonacci-like in digits": start with a(1)=1, a(2)=4; repeatedly adjoin digits of sum of previous two terms.

1, 4, 5, 9, 1, 4, 1, 0, 5, 5, 1, 5, 1, 0, 6, 6, 6, 1, 6, 1, 2, 1, 2, 7, 7, 7, 3, 3, 3, 9, 1, 4, 1, 4, 1, 0, 6, 6, 1, 2, 1, 0, 5, 5, 5, 5, 1, 6, 1, 2, 7, 3, 3, 1, 5, 1, 0, 1, 0, 1, 0, 6, 7, 7, 3, 9, 1, 0, 6, 4, 6, 6, 1, 1, 1, 1, 1, 6, 1, 3, 1, 4, 1, 0, 1, 2, 1, 0, 1, 6, 1, 0, 1, 0, 1, 2, 7, 2, 2, 2, 2, 7, 7, 4, 4