

A335854


The digitalroot sandwiches sequence (see Comments lines for definition).


3



11, 9, 99, 999, 9999, 9990, 1, 112, 12, 3, 125, 33, 4, 15, 8, 337, 44, 5, 154, 88, 2, 37, 24, 49, 55, 6, 14, 38, 81, 22, 53, 7, 92, 48, 495, 552, 66, 71, 47, 387, 813, 227, 531, 77, 79, 26, 483, 45, 152, 86, 64, 715, 471, 376, 83, 52, 73, 51, 87, 75, 792, 261, 43, 74, 56, 121, 863, 642, 759, 41, 436, 58, 385, 29
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OFFSET

1,1


COMMENTS

Imagine we would have a pair of adjacent integers in the sequence like [1951, 2020]. A digitalroot sandwich would then be made of the rightmost digit of a(n), the leftmost digit of a(n+1) and, in between, the digital root of their sum. The pair [1951, 2020] would then produce the DRsandwich 132. Please note that the pair [2020, 1951] would produce the genuine DRsandwich 011 (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..428


EXAMPLE

The first successive sandwiches are: 119, 999, 999, 999, 999, 011, 121, 231, ...
The first one (119) is visible between a(1) = 11 and a(2) = 9; we get the sandwich by inserting the digital root of the sum 1 + 9 = 10 (which is 1) between 1 and 9.
The second sandwich (999) is visible between a(2) = 9 and a(3) = 99; we get the sandwich by inserting the digital root of the sum 9 + 9 = 18 (which is 9) between 9 and 9.
The third sandwich (999) is visible between a(3) = 99 and a(3) = 999; we get the sandwich by inserting the digital root of the sum 9 + 9 = 18 (which is 9) between 9 and 9.
(...)
The sixth sandwich (011) is visible between a(6) = 9990 and a(7) = 1; we get the sandwich by inserting the digital root of the sum 0 + 1 = 1 (which is 1) between 0 and 1; etc.
The successive sandwiches rebuild, digit after digit, the starting sequence.


CROSSREFS

Cf. A335600 (first definition of such a sandwich) and A010888 (digital root of n).
Sequence in context: A072208 A210284 A219746 * A220664 A038323 A121154
Adjacent sequences: A335851 A335852 A335853 * A335855 A335856 A335858


KEYWORD

base,nonn


AUTHOR

Carole Dubois and Eric Angelini, Jun 26 2020


STATUS

approved



