[seqfan] From N to twice N by adding

[Eric Angelini]

Hello SeqFans,
This is my last post on the subject -- I have 
the impression I'm kind of spamming...

The general idea (an integer N leads to
the next one by adding to N one of it's
digits -- then iterate) could produce à few
sequences like those below (not sure at
all they are sound and/or without "holes"):

1) integers with no ancestor:
1,3,5,7,9,21,43,65,87,... (fini?)
2) integers with exactly one ancestor:
2,4,6,8,10,11,13,15,17,19,23,25,27,29,30,...
3) integers with exactly two ancestors:
12,20,24,...
4)integers with exactly three ancestors:
14,16,18,22,26,28,...
5) integers with exactly four ancestors:
126,128,...

[an ancestor is an integer that can
immediately produce another one:
126 has four (different) ancestors:
118+8=126
123+3=126
124+2=126
125+1=126
... they are thus {118,123,124,125}
]

Now the title of the post < From N to 2N by adding >
 -- here is a small table (condensed notation):

1+1=2
2+2=4
...
9+9=18
10+1=11+1=12+2=14+1=15+5=20
11+1=12+2=14+1=15+1=16+6=22
12+1=13+3=16+1=17+7=24
13+3=16+1=17+1=18+8=26
14+4=18+8=26+2=28
15+5=20+2=22+2=24+4=28+2=30
15+1=16+6=22+2=24...
15+1=16+1=17+7=24...
16+6=22+2=24+2=26+6=32
17+1=18+8=26+6=32+2=34
18+8=26+2=28+8=36
19+1=20+2=22+2=24+2=26+6=32+2=34+4=38
20+2=22+2=24+2=26+6=32+3=35+5=40
etc.

Some integers reach their double by
adding always the greatest digit -- 42 is an example:
42+4=46+6=52+5=57+7=64+6=70+7=77+7=84 (hit)
This is also true for 46:
46+6=52+5=57+7=64+6=70+7=77+7=84+8=92 (hit)
And for 52:
52+5=57+7=64+6=70+7=77+7=84+8=92+9=101+1=102+2=104 (hit)

What would be the sequence of such
"doublers by MAXdigit"? I guess it starts with:
TwiceMAX = 1,2,3,4,5,6,7,8,9,42,46,52,...

And TwiceMIN (same idea, but adding
the smallest digit all the time -- remembering
that 0 is the smallest digit of 10, for
instance):
1,2,3,4,5,6,7,8,9,33,36,39,...

Best,
É.