[seqfan] Write the sum of a+b with the digits involved in a+b

[Eric Angelini]

Hello SeqFans,
Here is my try (always use the smallest integer not used so far in the seq):
S=1,10,2,19,78,100,3,20,4,30,5,40,6,50,7,60,8,70,9,80,...

We see that the result of 1+10 uses only digits of the set {1,1,0}
The same with 10+2 which use some elements of {1,0,2}
Again, 2+19 uses elements of {2,1,9} for its result
And I guess 78 is the smallest integer respecting the constraint
(we see that 19+78 is 97 which uses for its transcription only
a few elements of {1,9,7,8}

Could someone check the existing terms, please, and extend
(if of interest)?

Best,
E.
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P.-S.
The set {0,1,2,3} does not permit to write 110, for instance.