A336874 The self-sandwiches sequence (see Comments lines for definition).

11, 2, 21, 212, 22, 222, 1, 2221, 112, 12, 122, 1221, 221, 12212, 121, 1121, 1210, 220, 110, 111, 113, 223, 114, 224, 115, 225, 226, 116, 227, 228, 117, 229, 2211, 3, 31, 312, 32, 23, 2123, 2231, 2122, 2120, 118, 119, 22111, 1111

Offset: 1

Author

Eric Angelini and Carole Dubois, Aug 06 2020

Keywords

• base
• nonn

Comments

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).

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.

The authors are unable to compute more terms than the ones proposed here and ask the readers' indulgence.

Examples

			The first successive sandwiches are: 112, 212, 122, 222, 212,...
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.
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.
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.
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..
The successive sandwiches rebuild, digit by digit, the starting sequence.
		

Crossrefs

Cf. A335600 (first sequence of this kind, linked to many others).