Thanks a lot, Mike. EA:

Are there integers leading to infinite sequences?

Mike:

no, you can never increase the number of digits. (...)

--- Edwin Clark has kindly computed this: n = 1, max num iterations jump = 1, final value = 1 n = 10, max num iterations jump = 2, final value = 11 n = 12, max num iterations jump = 7, final value = 33 n = 18, max num iterations jump = 8, final value = 44 n = 100, max num iterations jump = 20, final value = 222 n = 200, max num iterations jump = 42, final value = 444 n = 201, max num iterations jump = 43, final value = 444 n = 1000, max num iterations jump = 377, final value = 4444 n = 10000, max num iterations jump = 2926, final value = 44444 n = 100000, max num iterations jump = 23541, final value = 444444 Best, É.