|
%I #10 Jul 02 2020 05:21:47
%S 11,9,99,999,9999,9990,1,112,12,3,125,33,4,15,8,337,44,5,154,88,2,37,
%T 24,49,55,6,14,38,81,22,53,7,92,48,495,552,66,71,47,387,813,227,531,
%U 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
%N The digital-root sandwiches sequence (see Comments lines for definition).
%C Imagine we would have a pair of adjacent integers in the sequence like [1951, 2020]. A digital-root 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 DR-sandwich 132. Please note that the pair [2020, 1951] would produce the genuine DR-sandwich 011 (we keep the leading zero: these are sandwiches after all, not integers).
%C 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.
%H Carole Dubois, <a href="/A335854/b335854.txt">Table of n, a(n) for n = 1..428</a>
%e The first successive sandwiches are: 119, 999, 999, 999, 999, 011, 121, 231, ...
%e 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.
%e 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.
%e 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.
%e (...)
%e 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.
%e The successive sandwiches rebuild, digit after digit, the starting sequence.
%Y Cf. A335600 (first definition of such a sandwich) and A010888 (digital root of n).
%K base,nonn
%O 1,1
%A _Carole Dubois_ and _Eric Angelini_, Jun 26 2020
|
