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A336904 The natural sandwiches sequence (see Comments lines for definition). 1
11, 2, 22, 223, 23, 4, 235, 44, 6, 25, 7, 448, 66, 9, 2510, 77, 1, 14, 8, 12, 661, 3, 99, 1420, 15, 771, 61, 117, 141, 88, 81, 91, 220, 612, 13, 32, 29, 92, 310, 24, 152, 5, 71, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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 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).

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.

LINKS

Carole Dubois, Table of n, a(n) for n = 1..5001

EXAMPLE

The first successive sandwiches are: 112, 222, 232, 342, 354, 462,...

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.

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.

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;

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.

The successive sandwiches rebuild, digit by digit, the starting sequence.

CROSSREFS

Cf. A335600.

Sequence in context: A336874 A040120 A176592 * A051309 A077344 A298439

Adjacent sequences:  A336901 A336902 A336903 * A336905 A336906 A336907

KEYWORD

base,nonn

AUTHOR

Carole Dubois and Eric Angelini, Aug 07 2020

STATUS

approved

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Last modified September 24 21:05 EDT 2021. Contains 347651 sequences. (Running on oeis4.)