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A322467 Lexicographically first sequence of distinct terms such that a(n) is duplicated a(n) digits to the right.

%I A322467 #5 Jan 15 2019 20:27:17
%S A322467 1,10,2,3,20,30,5,6,4,105,46,7,11,8,12,9,70,208,21,190,120,130,13,14,
%T A322467 15,17,18,22,16,131,140,154,61,71,181,60,32,23,24,27,28,29,31,35,25,
%U A322467 36,40,170,42,302,41,43,270,280,292,531,110,53,54,613,62,160,400,47,104,200,410,34,300,19,38,1200,44,33,37,45
%N A322467 Lexicographically first sequence of distinct terms such that a(n) is duplicated a(n) digits to the right.
%C A322467 This sequence is conjectured to be a permutation of the positive integers.
%H A322467 Jean-Marc Falcoz, <a href="/A322467/b322467.txt">Table of n, a(n) for n = 1..1501</a>
%e A322467 The sequence starts with 1,10,2,3,20,30,5,6,4,105,...
%e A322467 a(1) = 1 forces the next digit to be 1;
%e A322467 a(2) = 10 as 10 is the smallest available integer starting with 1 and not leading to a contradiction; this 10 will be duplicated 10 digits to the right;
%e A322467 a(3) = 2 as 2 is the smallest available integer not leading to a contradiction; this 2 will be duplicated 2 digits to the right;
%e A322467 a(4) = 3 as 3 is the smallest available integer not leading to a contradiction; this 3 will be duplicated 3 digits to the right;
%e A322467 a(5)= 20 as 20 is the smallest available integer starting with 2 and not leading to a contradiction; this 20 will be duplicated 20 digits to the right;
%e A322467 a(6) = 30 as 30 is the smallest available integer starting with 3 and not leading to a contradiction; this 30 will be duplicated 30 digits to the right;
%e A322467 Could a(7) be equal to 4? No, because this 4 cannot be duplicated 4 digits to the right as there is already a 0 there (this 0 comes from the duplicated 10);
%e A322467 Thus a(7) = 5 as 5 is the smallest available integer not leading to a contradiction; this 5 will be duplicated 5 digits to the right;
%e A322467 Could a(8) be equal to 4? No, because this 4 cannot be duplicated 4 digits to the right as there is already a 5 there (this 5 comes from the duplicated 5);
%e A322467 Thus a(8) = 6 as 6 is the smallest available integer not leading to a contradiction; this 6 will be duplicated 6 digits to the right;
%e A322467 a(9) = 4 as 4 is the smallest available integer not leading to a contradiction; this 4 will be duplicated 4 digits to the right;
%e A322467 a(10) = 105 as 105 is the smallest available integer starting with 10, followed by 5, and not leading to a contradiction; this 105 will be duplicated 105 digits to the right.
%e A322467 Etc.
%K A322467 base,nonn
%O A322467 1,2
%A A322467 _Jean-Marc Falcoz_ and _Eric Angelini_, Dec 09 2018