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The digital sum of a(n) is not a substring of a(n+1), a(n+1) being the smallest integer not yet present in the sequence that doesn't lead to a contradiction.
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%I #15 Apr 11 2018 10:35:39

%S 1,2,3,4,5,6,7,8,9,10,20,11,13,12,14,16,15,17,19,18,21,22,23,24,25,26,

%T 27,28,29,30,40,31,32,33,34,35,36,37,38,39,41,42,43,44,45,46,47,48,49,

%U 50,60,51,52,53,54,55,56,57,58,59,61,62,63,64,65,66,67,68,69,70,80,71,72,73,74,75,76,77

%N The digital sum of a(n) is not a substring of a(n+1), a(n+1) being the smallest integer not yet present in the sequence that doesn't lead to a contradiction.

%C a(1) = 1, and for n > 1 a(n) is the smallest integer not yet present in the sequence such that the digital sum of a(n-1) is not a substring of the decimal digits of a(n).

%H Lars Blomberg, <a href="/A302589/b302589.txt">Table of n, a(n) for n = 1..10000</a>

%e The digital sum of 1 is 1, so a(2) = 2 is the first unused number not containing a "1"; the digital sum of 2 is 2, so a(3) = 3 is the first unused number not containing a "2"; ...; the digital sum of 10 is 1, so a(11) = 20 is the first unused number not containing a "2" (2 is already used); etc.

%Y Cf. A173821 (where a(n) IS a substring of a(n+1)).

%K nonn,base

%O 1,2

%A _Eric Angelini_ and _Lars Blomberg_, Apr 10 2018