[seqfan] Concatenate the sums of the neighboring digits

[Éric Angelini]

Hello SeqFans,
Take 567
Keep the sums of the neighboring digits:
5+6 = 11 and 6+7 = 13
Concatenate the results:
1113
Iterate from there:
1113 --> 224 --> 46 --> 10 --> 1 -->
END

If instead of 567 we take 5677 another
story appears:
5 6 7 7
11 13 14
2 2 4 4 5
4 6 8 9
10 14 17
1 1 5 5 8
2 6 10 13
8 7 1 1 4
15 8 2 5
6 13 10 7
7 4 4 1 7
11 8 5 8
2 9 13 13
11 10 4 4 4
2 2 1 4 8 8
4 3 5 12 16
7 8 6 3 3 7
...
Will this end at some point?
Enter in a loop? Grow forever?
What is known about this transform?
Best,
É.