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

[Michael Branicky]

Computer is saying that 17117 works

and that records in cardinality occur as follows
FOUND 1 1 {1} FOUND 112 2 {2, 4} FOUND 139 3 {8, 4, 7} FOUND 219 4 {8, 2,
4, 6} FOUND 373 5 {1, 2, 4, 6, 8} FOUND 719 6 {0, 2, 4, 6, 8, 9} FOUND 1133
7 {0, 2, 4, 6, 7, 8, 9} FOUND 1919 8 {0, 2, 4, 5, 6, 7, 8, 9} FOUND 3377 9
{0, 2, 3, 4, 5, 6, 7, 8, 9} FOUND 17117 10 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

On Mon, Apr 3, 2023 at 3:07 PM Neil Sloane <njasloane at gmail.com> wrote:

> 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.
>
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>