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%I #5 Aug 16 2020 12:57:26
%S 11,2,21,212,22,222,1,2221,112,12,122,1221,221,12212,121,1121,1210,
%T 220,110,111,113,223,114,224,115,225,226,116,227,228,117,229,2211,3,
%U 31,312,32,23,2123,2231,2122,2120,118,119,22111,1111
%N The self-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 single digit d of the sequence itself not been yet duplicated inside a sandwich. The pair [1951, 2020] would then produce the sandwich 1d2. Please note that the pair [2020, 1951] would produce the genuine sandwich 0d1 (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.
%C The authors are unable to compute more terms than the ones proposed here and ask the readers' indulgence.
%e The first successive sandwiches are: 112, 212, 122, 222, 212,...
%e The 1st one (112) is visible between a(1) = 11 and a(2) = 2; we get the sandwich by inserting the 1st digit of the sequence itself, 1.
%e The 2nd sandwich (212) is visible between a(2) = 2 and a(3) = 21; we get this sandwich by inserting inserting the 2nd digit of the sequence itself, 1.
%e The 3rd sandwich (122) is visible between a(3) = 21 and a(4) = 212; we get this sandwich by inserting the 3rd digit of the sequence itself, 2.
%e The 4th sandwich (222) is visible between a(4) = 212 and a(5) = 22; we get this sandwich by inserting the 4th digit of the sequence itself, 2. Etc..
%e The successive sandwiches rebuild, digit by digit, the starting sequence.
%Y Cf. A335600 (first sequence of this kind, linked to many others).
%K base,nonn
%O 1,1
%A _Eric Angelini_ and _Carole Dubois_, Aug 06 2020
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