[seqfan] Another Split & Multiply sequence from Eric A.

[Neil Sloane]

Eric Angelini recently posted something that led to the creation of
A361337.  These are the numbers which can reach 0 after a suitable series
of split-and-multiply operations.

I just stumbled across an older email from him where he asks if there are
any numbers which can reach all of 0, 1, 2, ..., 9 by suitable sequences of
split-and-multiply.  (See A361337 for the precise rules).

I quote from Eric's email:
Take the integer 1133
We split 1133 into 1 and 133 for instance (inserting a star between two
digits).
(a star means multiply)
We then make 1*133 = 133
We iterate until we get a single digit.

Question:
Is there an integer that can reach any of the 10 single digits?
With 1133 we can reach 0, 4, 7, 8 or 9:
1133 -> 11*33 -> 36*3 -> 10*8 -> 8*0 -> 0
1133 -> 11*33 -> 3*63 -> 1*89 -> 8*9 -> 7*2 -> 1*4 -> 4
1133 -> 113*3 -> 3*39 -> 1*17 -> 1*7 -> 7
1133 -> 113*3 -> 3*39 -> 11*7 -> 7*7 -> 4*9 -> 3*6 -> 1*8 -> 8
1133 -> 1*133 -> 1*33 -> 3*3 -> 9

P.S. We don’t insert a star before a zero.

I couldn’t find any such number.