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The a(n)-th digit of the sequence is present in a(n+1). Lexicographically earliest sequence of distinct terms > 0 with this property.
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%I #18 Feb 24 2021 12:07:54

%S 1,10,2,11,3,20,23,4,12,14,21,5,251,40,6,13,15,16,24,30,17,22,61,7,31,

%T 26,18,19,25,36,41,51,27,73,8,28,71,9,50,90,80,29,35,120,32,42,37,47,

%U 81,60,57,45,52,53,33,34,38,62,39,72,70,100,125,43,63,48,58,91,101,83,82,93,102,103

%N The a(n)-th digit of the sequence is present in a(n+1). Lexicographically earliest sequence of distinct terms > 0 with this property.

%C This sequence is conjectured to be a permutation of the positive integers.

%H Carole Dubois, <a href="/A341816/b341816.txt">Table of n, a(n) for n = 1..5001</a>

%H Carole Dubois, <a href="/A341816/a341816.jpg">Scatterplot even-row terms vs. odd-row terms</a>

%e a(1) = 1, "The 1st digit of the sequence is present in a(2)"; true, 1 is in 14;

%e a(2) = 10, "The 10th digit of the sequence is present in a(3)"; true, 2 is in 2;

%e a(3) = 2, "The 2nd digit of the sequence is present in a(4)"; true, 1 is in 11;

%e a(4) = 11, "The 11th digit of the sequence is present in a(5)"; true, 3 is in 3;

%e a(5) = 3, "The 3rd digit of the sequence is present in a(6)"; true, 0 is in 20;

%e a(6) = 20, "The 20th digit of the sequence is present in a(7)"; true, 2 is in 23;

%e a(7) = 23, "The 23rd digit of the sequence is present in a(8)"; true, 4 is in 4; etc.

%Y Cf. A000027 (the positive integers).

%K base,nonn

%O 1,2

%A _Eric Angelini_ and _Carole Dubois_, Feb 20 2021