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%I #14 Sep 05 2020 06:53:32
%S 11,2,22,223,23,4,235,44,6,25,7,448,66,9,2510,77,1,14,8,12,661,3,99,
%T 1420,15,771,61,117,141,88,81,91,220,612,13,32,29,92,310,24,152,5,71,
%U 26,6127,17,28,112,98,830,813,19,132,20,33,62,34,133,53,236,293,79,238,30,39,2440,124,155,42,714
%N The natural 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, the smallest natural number N not yet inserted into a sandwich. The pair [1951, 2020] would then produce the natural sandwich 1N0. Please note that the pair [2020, 1951] would produce the genuine sandwich 0N1 (we keep the leading zero: these are sandwiches after all, not integers).
%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="/A336904/b336904.txt">Table of n, a(n) for n = 1..5001</a>
%e The first successive sandwiches are: 112, 222, 232, 342, 354, 462,...
%e The 1st one (112) is visible between a(1) = 11 and a(2) = 2; we get the sandwich by inserting 1 between 1 and 2.
%e The 2nd sandwich (222) is visible between a(2) = 2 and a(3) = 22; we get this sandwich by inserting 2 between 2 and 2.
%e The 3rd sandwich (232) is visible between a(3) = 22 and a(4) = 223; we get this sandwich by inserting 3 between 2 and 2;
%e The 4th sandwich (342) is visible between a(4) = 223 and a(5) = 23; we get this sandwich by inserting 4 between 3 and 2; etc.
%e The successive sandwiches rebuild, digit by digit, the starting sequence.
%Y Cf. A335600.
%K base,nonn
%O 1,1
%A _Carole Dubois_ and _Eric Angelini_, Aug 07 2020
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