[seqfan] Stappled sequence

[Eric Angelini]

Hello SeqFans,
Rule1:
a(n) and a(n+1) are always united by a "stapple";
Rule2:
the two extremities of a stapple cross identical digits;
Rule3:
no digit is involved in more than one
stapple.
Rule4:
the seq is always extended with the smallest
integer no yet present and not leading to
a contradiction.

S=1,10,20,12,11,13,23,21,14,24,22,25,15,
16,26,27,17,18,28,29,19,31,30,40,34,32,
42,41,51,35,33,36,46,43,37,47,44,...

Example:
1 and 10 = stapple 1-1
10 and 20 = stapple 0-0
20 and 12 = stapple 2-2
(the seq is not extended here with
the integer "2" as the digit "2" would be stappled twice)
12 and 11 = stapple 1-1
11 and 13 = stapple 1-1 (all 1's are different)
13 and 23 = stapple 3-3
etc.

When it comes to integers > 99,
one or more digits of a(n) will not
be involved in any stapple at all.
But the 4 rules above must still apply.

Best,
É.