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%I #8 Sep 06 2020 04:58:48
%S 1,2,22,220,3,33,330,4,44,440,5,55,550,6,66,660,7,77,770,8,88,880,9,
%T 99,990,10,11,12,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,
%U 31,32,34,35,36,37,38,39,40,41,42,43,45,46,47,48,49,50,51,52,53,54,56,57,58,59,60,61,62,63,64,65,67,68
%N The empty sandwiches sequence (see Comments lines for definition).
%C Imagine we would have a pair of adjacent integers in the sequence like [1951, 2020]. The sandwich would then be made of the rightmost digit of a(n), the leftmost digit of a(n+1) and, in between, some combination c of those two digits (see A335600 for instance). The pair [1951, 2020] would then produce the sandwich 1c2. Please note that the pair [2020, 1951] would produce the genuine sandwich 0c1 (we keep the leading zero: these are sandwiches after all, not integers).
%C In this sequence we don't insert anything between the two "slices of bread": there is no c, the sandwiches are empty.
%C Now we want the sequence to be the lexicographically earliest sequence of distinct positive terms such that the successive sandwiches emerging from the sequence rebuild it, digit after digit.
%H Carole Dubois, <a href="/A336894/b336894.txt">Table of n, a(n) for n = 1..113</a>
%e The first successive sandwiches are: 12, 22, 22, 03, 33, 33, 04,...
%e The 1st one (12) is visible between a(1) = 1 and a(2) = 2.
%e The 2nd one (22) is visible between a(2) = 2 and a(3) = 22.
%e The 3rd one (22) is visible between a(3) = 22 and a(4) = 220.
%e The 4th one (03) is visible between a(4) = 220 and a(5) = 3; etc.
%e The successive sandwiches rebuild, digit by digit, the starting sequence.
%Y Cf. A335600.
%K base,nonn
%O 1,2
%A _Eric Angelini_ and _Carole Dubois_, Aug 07 2020