Fibonacci Number Problems

[SavVyhelps]

you are the only youtuber who most explained fibonnaci problems so clearly...you are so great..thank you so much..bless you

[faery]

Thank you very much. You discussed it very clearly.

[alexiscorona]

Thank you for this! Now I finally undertand it.

[chrisg]

I've been looking into those Fibonacci numbers Fn which when added to their reverse are divisible exactly by n. For example F11 is 89, 89+98 = 187, 187/11 = 17. The only others I found thus far are F1 (1), F2 (1), F5 (5),  F10 (55),  F16 (987), F26(121393), F46 (1836311903). Is there a pattern? Obviously the results are going to depend on the base you're using, here decimal.