An add-largest-digit sequence in base 10 is defined for some n by the recursive rule
a1=n,
at=at-1+[the largest digit of at-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?
If a term ends in 9 then the next term will end in 8, breaking the streak of odd value terms.
If a term ends in 1 then in at most two terms we will have an even value.
Finally, for a sequence of odd terms they will all have the same difference between terms. Since there are five odd digits then the longest string of odd value terms is five terms.
Example: 798 -> 807 -> 815 -> 823 -> 831 -> 839 -> 848
Solution
