An add-largest-digit sequence in base 10 is defined for some n by the recursive rule

a₁=n,
a_t=a_t-1+[the largest digit of a_t-1] for t>1

For example, if n=165 the sequence begins 165, 171, 178, 186, 194, 203, 206, 212, 214, ...

What is the greatest number of successive odd terms that can be found in an add-largest-digit sequence?