Sliding numbers

[Eric Angelini]

Hello SeqFan and Math-fun,

Let's start with an example of "sliding number":

1/4 + 1/25 = 0.29  --> 29 is a "sliding number"
1/8 + 1/125 = 0.133 --> 133 is a "sliding number"
1/2 + 1/5 = 0.7 --> 7 is a "sliding number"
etc.

Note that :

1/20 + 1/50 = 0.70 --> 70 is a "sliding number"
though 0.70 is usually written 0.7

So any "sliding number" G produces an infinite
quantity of others : Gx10, Gx100, Gx1000, etc.

Generally speaking we have this:

1/a + 1/b = (a+b)/10^k     [with k=1,=2,=3,=4, ...]
--> the "sliding number" G = a+b

My pb is to build a correct seq. of G's (how not
to forget any G behind?)

By hand I've proceeded so:

  10 --> 1+10   --> G(2)=11
         2+5    --> G(1)=7
 100 --> 1+100  --> G(7)=101
         2+50   --> G(6)=52
         4+25   --> G(5)=29
         5+20   --> G(4)=25
         10+10  --> G(3)=20
1000 --> 1+1000 --> G(15)=1001
         2+500  --> G(14)502
         4+250  --> G(13)=254
         5+200  --> G(12)=205
         8+125  --> G(11)133
         10+100 --> G(10)=110
         20+50  --> G(9)=70
         25+40  --> G(8)=65

... but you see now my pb: G(8) and G(9) are < G(7) !
I have to rename them...

The sequence would then start like this:

7,11,20,25,29,52,65,70,101,110,133,205...

BUT:

10000 --> 100+100 (among others) which gives G=200...

So I have to correct the sequence and insert 200:

7,11,20,25,29,52,65,70,101,110,133,200,205...

[BTW 200 is G(3)x10]

Could someone compute enough terms to be submitted
to the OEIS without leaving any G integer behind?

Many thanks,
É.
-----------
PS. I don't know who has given the name "sliding
numbers" to those integers -- I might have read
that on the Internet somewhere around 1997...
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