A336894 The empty sandwiches sequence (see Comments lines for definition).

1, 2, 22, 220, 3, 33, 330, 4, 44, 440, 5, 55, 550, 6, 66, 660, 7, 77, 770, 8, 88, 880, 9, 99, 990, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 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

Offset: 1

Author

Eric Angelini and Carole Dubois, Aug 07 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, 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).

In this sequence we don't insert anything between the two "slices of bread": there is no c, the sandwiches are empty.

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.

Examples

			The first successive sandwiches are: 12, 22, 22, 03, 33, 33, 04,...
The 1st one (12) is visible between a(1) = 1 and a(2) = 2.
The 2nd one (22) is visible between a(2) = 2 and a(3) = 22.
The 3rd one (22) is visible between a(3) = 22 and a(4) = 220.
The 4th one (03) is visible between a(4) = 220 and a(5) = 3; etc.
The successive sandwiches rebuild, digit by digit, the starting sequence.
		

Links

• Carole Dubois, Table of n, a(n) for n = 1..113

Crossrefs

Cf. A335600.