[seqfan] Re: List the dividers, sum the digits

[Frank Adams-Watters]

The digit sum of 1,13 is 5, not 14. I get

10 -> 9 -> 13 -> 5 -> 6 -> 12 -> 19 -> 11 -> 3 -> 4 -> 7 -> 8 -> 15

Any loops are going to contain only small numbers; the digit sum reduces large numbers by a lot. Everything up to 13 is covered by the example above (adding 2 -> 3).

We have 14 -> 15; 16 -> 22 -> 9, 17 -> 9, 18 -> 30 -> 27 -> 22, and 20 -> 15, so everything 1 to 20 gets to 15.

I suspect 1 and 15 are the only loops.

Franklin T. Adams-Watters


-----Original Message-----
From: Eric Angelini <Eric.Angelini at kntv.be>
To: Sequence Discussion list <seqfan at list.seqfan.eu>
Sent: Sat, Nov 7, 2015 4:46 pm
Subject: [seqfan] List the dividers, sum the digits



Hello SeqFans,
1) list all dividers of A (1 and A included) ;
2) sum all
digits of the above list ;
3) iterate

Example for A=10:
10--> 1,10,2,5
dig.sum=9
 9--> 1,9,3      dig.sum=13
13--> 1,13       dig.sum=14
14-->
1,14,2,7 dig.sum=15
15--> 1,15,3,5 dig.sum=15 (fixed point)