A335886 The heavy sandwiches sequence (see Comments lines for definition).

1, 2, 22, 4, 228, 44, 8, 28, 3, 24, 43, 288, 16, 282, 433, 6, 241, 64, 36, 2881, 61, 222, 84, 31, 86, 612, 21, 66, 41, 23, 6122, 166, 12, 221, 68, 412, 318, 863, 662, 42, 1666, 244, 122, 3186, 2216, 6124, 216, 683, 242, 63, 864, 83, 18, 62, 842, 2161, 224, 4126, 361, 226, 366, 48, 26, 3663, 622, 126, 32, 484

Offset: 1

Author

Eric Angelini and Carole Dubois, Jun 28 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 product of those two digits. The pair [1951, 2020] would then produce the sandwich 122. Please note that the pair [2020, 1951] would produce the genuine sandwich 001 (we keep the leading zeros: 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.

Examples

			The first successive sandwiches are: 122, 242, 284, 482, 8324, ...
The first one (122) is visible between a(1) = 1 and a(2) = 2; we get the sandwich by inserting the product 2 between 1 and 2.
The second sandwich (242) is visible between a(2) = 2 and a(3) = 22; we get this sandwich by inserting the product 4 between 2 and 2.
The third sandwich (284) is visible between a(3) = 22 and a(4) = 4; we get this sandwich by inserting the product 8 between 2 and 4.
The fourth sandwich (482) is visible between a(4) = 4 and a(5) = 228; we get this sandwich by inserting the product 8 between 4 and 2.
The fifth sandwich (8324) is visible between a(5) = 228 and a(6) = 44; we get this sandwich by inserting the product 32 between 8 and 4; etc.
The successive sandwiches rebuild, digit by digit, the starting sequence.
		

Links

• Carole Dubois, Table of n, a(n) for n = 1..611

Crossrefs

Cf. A335600 (the "poor" sandwich sequence).