# [seqfan] Weird digit addition -- and integers failing at it

Eric Angelini Eric.Angelini at kntv.be
Sun Mar 18 17:55:31 CET 2012

```Hello SeqFans,

Let's write down an AB integer (2 digits, A and B) using a square
per digit and decide to write the result of the addition of A+B
on the first 'x' mark, or on the two 'x' marks if needed,
like this (again, one digit per square):
A B
. x
. x
So 10 produces 10
.1
And 19 produces 19
.1
.0
Now, sometimes we are forced to repeat the addition, as a new
integer appears, having more than one digit:

123 produces 35 and 35 produces 8:  123
.35
..8
193 produces this 'array':    193
.11
.02
..2

But 192 and 194, for instance, fail:   192   194
.11   .11
.01   .01
... as 11 shoud produce 11
.2  <--- and not .1 (like above)

The sequence of "failing integers" starts with 127, I guess:

128
.31
..0 <-- the zero, here, should be a 4, resulting from 3+1).

Could someone compute a few hundred terms of this "failing integers"
sequence (if of some interest)?

Puzzle:
What is the biggest integer _having no zero_ that is NOT failing?
I have 5121212:

5121212
.633333
..96666
...1111
...5222
....744
.....18
.....19
......1
......0

Best,
É.

```