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%I #8 Jun 02 2020 14:20:06
%S 1,9,10,8,12,6,16,2,18,27,28,14,3,36,40,5,42,4,17,45,46,20,15,48,21,
%T 22,24,11,54,63,64,26,72,81,82,30,23,84,33,85,32,88,29,90,99,100,35,
%U 105,25,41,108,117,118,44,120,34,53,126,130,50,135,136,56,51,144,153,154,62,156,52,71,160,38,162,168,39
%N Lexicographically earliest sequence of distinct positive integers such that the digital root of the cumulative sum so far divides a(n).
%H Carole Dubois, <a href="/A334681/b334681.txt">Table of n, a(n) for n = 1..5001</a>
%e The sequence starts hereunder with the S line (this sequence); then comes the Q line (cumulative sum of S' terms); then comes the R line (digital root of Q at this point):
%e S = 1, 9, 10, 8, 12, 6, 16, 2, 18, 27, 28, 14, 3, 36, 40,...
%e Q = 1, 10, 20, 28, 40, 46, 62, 64, 82, 109, 137, 151, 154, 190, 230,...
%e R = 1, 1, 2, 1, 4, 1, 8, 1, 1, 1, 2, 7, 1, 1, 5,...
%e We see that the term R divides the term S on top of the 3-level column.
%Y Cf. A010888 (digital root of n).
%K base,nonn
%O 1,2
%A _Eric Angelini_ and _Carole Dubois_, May 08 2020
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