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

[hv at crypt.org]

Neil Sloane <njasloane at gmail.com> wrote:
: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).

The first example appears to be 17117:

0: 1*7117 => 7*117 => 8*19 => 1*52 => 5*2 => 1*0 => 0
1: 1711*7 => 1197*7 => 837*9 => 7*533 => 373*1 => 37*3 => 1*11 => 1*1 => 1
2: 1*7117 => 711*7 => 4*977 => 3*908 => 2*724 => 14*48 => 67*2 => 1*34
   => 3*4 => 1*2 => 2
3: 1*7117 => 711*7 => 49*77 => 377*3 => 1*131 => 1*31 => 3*1 => 3
4: 1*7117 => 711*7 => 4*977 => 3*908 => 2*724 => 144*8 => 11*52 => 57*2
   => 1*14 => 1*4 => 4
5: 1711*7 => 119*77 => 91*63 => 573*3 => 171*9 => 153*9 => 137*7 => 9*59
   => 5*31 => 15*5 => 7*5 => 3*5 => 1*5 => 5
6: 1*7117 => 7*117 => 81*9 => 72*9 => 6*48 => 28*8 => 2*24 => 4*8 => 3*2 => 6
7: 1711*7 => 1197*7 => 837*9 => 7*533 => 37*31 => 11*47 => 51*7 => 3*57
   => 1*71 => 7*1 => 7
8: 1*7117 => 7*117 => 81*9 => 72*9 => 6*48 => 2*88 => 1*76 => 7*6 => 4*2 => 8
9: 1*7117 => 711*7 => 49*77 => 377*3 => 113*1 => 11*3 => 3*3 => 9

Hugo