
COMMENTS

The next candidate for a continuation is 154!1, which is composite with 272 decimal digits and unknown factorization. Further known terms are 157, 229, 381, 390, 392, 400, 814, 929; factorization unknown for 154, 196, 232, 271, 307, 322, 332, 333, 334, 350, 352, 386, 389, 443, 449, ...
Note that the two prime factors of 24!1 = 620448401733239439359999 = 625793187653 * 991459181683 both have 12 decimal digits.
There is another term with prime factors with equal number of decimal digits: 34!1 = 10398560889846739639*28391697867333973241 (20 digits each)
From Antti Karttunen, Dec 27 2015: (Start)
Furthermore, both factors of 24!1 are in binary system 40 bits long (A070939), and in factorial base representation (A007623) they both have 14 digits: <7,2,6,5,4,8,2,3,0,0,2,0,2,1> and <11,5,2,10,1,5,6,3,4,1,1,3,0,1>. That is, A007623(625793187653) = 72654823002021, but the latter number cannot be represented reliably in such a more compact form, because it already contains digits > 9.
Factors of 34!1 are 64 and 65 bits long, and their factorial base representations contain both 20 digits: <4,5,9,3,1,13,11,7,9,1,0,6,1,1,6,5,3,1,0,1> and <11,13,7,10,0,12,3,4,6,11,1,8,1,4,2,2,1,2,2,1>.
Also the factors of 5!1 = 119 = 7*17 are both of the same length in factorial base system: "101" and "221".
(End)
1338, 1447, 1788, 1824, 2805, 2881, 2960, 5824 are also terms of the sequence.  Chai Wah Wu, Feb 28 2020
