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A294069 The smallest digit of a(n+1) is strictly smaller than the largest digit of a(n).

%I A294069 #20 Jun 02 2025 12:22:58
%S A294069 1,10,20,11,30,2,12,13,14,3,15,4,16,5,17,6,18,7,19,8,21,31,22,40,23,
%T A294069 24,25,26,27,28,29,32,41,33,42,34,35,36,37,38,39,43,50,44,51,45,46,47,
%U A294069 48,49,52,53,54,60,55,61,56,57,58,59,62,63,64,65,70,66
%N A294069 The smallest digit of a(n+1) is strictly smaller than the largest digit of a(n).
%C A294069 The sequence starts with a(1) = 1 and was always extended with the smallest integer not yet present and not leading to a contradiction.
%C A294069 From _Robert G. Wilson v_, Feb 07 2018: (Start)
%C A294069 Inverse: 1, 6, 10, 12, 14, 16, 18, 20, 2, 4, 7, 8, 9, 11, 13, 15, 17, 19, 3, ..., .
%C A294069 Permutation of the Integers.
%C A294069 (End)
%H A294069 Jean-Marc Falcoz, <a href="/A294069/b294069.txt">Table of n, a(n) for n = 1..10001</a>
%e A294069 The "0" of 10 is strictly < "1", which is the largest digit of 1;
%e A294069 The "0" of 20 is strictly < "1", which is the largest digit of 10;
%e A294069 The "1" of 11 is strictly < "2", which is the largest digit of 20;
%e A294069 The "0" of 30 is strictly < "1", which is the largest digit of 11;
%e A294069 The "2" of 2 is strictly < "3", which is the largest digit of 30;
%e A294069 The "1" of 12 is strictly < "2", which is the largest digit of 2; etc.
%t A294069 f[s_List] := Block[{k = 1, mx = Max@IntegerDigits@s[[-1]]}, While[MemberQ[s, k] || Min@IntegerDigits@k >= mx, k++]; Append[s, k]]; Nest[f, {1}, 80] (* _Robert G. Wilson v_, Feb 07 2018 *)
%Y A294069 Cf. A002283, A011540, A284062-A284069.
%K A294069 base,nonn
%O A294069 1,2
%A A294069 _Eric Angelini_ and _Jean-Marc Falcoz_, Feb 07 2018