[seqfan] Digit chain

[Eric Angelini]

Hello SeqFans,
if S is of interest, could please someone check, extend and submit to the OEIS?
Thanks,
Best,
É.

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S = 1,10,11,12,2,20,21,13,3,23,22,24,4,14,15,5,25,...

Lexicographically smallest permutation of the natural numbers such that in decimal representation a(n) shares at least one digit with a(n-1); a(1)=1.

In building S, always choose the smallest term not yet present in S and not leading to a contradiction.