[seqfan] Re: 10-line tables ?

[Lars Blomberg]

Hello,

I find the first 9-term solution
4899 -> 4 * 899
3596 -> 3 * 596
1788 -> 1 * 788
788 -> 7 * 88
616 -> 6 * 16
96 -> 9 * 6
54 -> 5 * 4
20 -> 2 * 0
0

And the first 10-term solution
9848 -> 9 * 848
7632 -> 7 * 632
4424 -> 4 * 424
1696 -> 1 * 696
696 -> 6 * 96
576 -> 5 * 76
380 -> 3 * 80
240 -> 2 * 40
80 -> 8 * 0
0 

Below 10^7 there are 11937 9-term solutions and 947 10-term solutions.

/Lars

-----Ursprungligt meddelande-----
Från: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] För Eric Angelini
Skickat: den 28 april 2015 20:06
Till: Sequence Fanatics Discussion list
Ämne: [seqfan] 10-line tables ?

Hello SeqFans,
Look at this 9 line-table:

131399 -> 1*31399 = 31399
31399  -> 3*1399 = 4197
4197   -> 4*197 = 788
788    -> 7*88 = 616
616    -> 6*16 = 96
96     -> 9*6 = 54
54     -> 5*4 = 20
20     -> 2*0 = 0
0

Is it possible to find a similar 10-line table where:

a) all lines start with a different digit;
b) the said digit, multiplied by the chain to its right, 
   gives the integer starting the next line;
c) no integer (except 0) has a leading zero.

Best,
É.






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