[seqfan] Re: Multiply my digits

[Lars Blomberg]

Another attack: since the 7-smooth numbers are (relatively) rare, I generated all with n digits and then successively multiply digits until a 1-digit number appears. No digit 0 is allowed.
I find the longest sequences as follows:
n is the number of digits in the next-to-last number, the concatenation of all prime factors in this number is the last number (whose digits may be permuted and still give a solution).
n=9
2,12,126,1792,1741824,368947264,22222277777777 
n=16
6,16,128,288,23328,2939328,1792336896,3416267673274176,2222223333333333333333333333333337
n=15
8,18,192,124416,1194891264,727326941773824,22222222222222222222222222222222222222233377
Interestingly, no other solutions were found for n <= 50.

/Lars