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A286890 a(n) is the least positive integer not yet in the sequence that shares its largest digit with that of a(n-1); a(1)=1.

%I A286890 #18 Aug 10 2017 11:13:39
%S A286890 1,10,11,12,2,20,21,22,23,3,13,30,31,32,33,34,4,14,24,40,41,42,43,44,
%T A286890 45,5,15,25,35,50,51,52,53,54,55,56,6,16,26,36,46,60,61,62,63,64,65,
%U A286890 66,67,7,17,27,37,47,57,70,71,72,73,74,75,76,77,78,8,18,28,38,48,58,68,80,81,82,83,84,85,86,87,88,89,9,19,29,39,49,59,69,79,90,91,92,93,94,95,96,97,98,99,109,119,129
%N A286890 a(n) is the least positive integer not yet in the sequence that shares its largest digit with that of a(n-1); a(1)=1.
%C A286890 After a(81) = 89, each term must contain a 9.
%C A286890 Unlike A184992, not a permutation of the positive integers, but contains all numbers from 1 to 99.
%H A286890 Jean-Marc Falcoz and Eric Angelini, <a href="/A286890/b286890.txt">Table of n, a(n) for n = 1..5001</a>
%e A286890 Gathering intervals of consecutive integers, sequence begins as follows:
%e A286890 1,                               10..12,
%e A286890 2,                               20..23,
%e A286890 3, 13,                           30..34,
%e A286890 4, 14, 24,                       40..45,
%e A286890 5, 15, 25, 35,                   50..56,
%e A286890 6, 16, 26, 36, 46,               60..67,
%e A286890 7, 17, 27, 37, 47, 57,           70..78,
%e A286890 8, 18, 28, 38, 48, 58, 68,       80..89,
%e A286890 9, 19, 29, 39, 49, 59, 69, 79,   90..99,
%e A286890 109, 119, 129, ...
%t A286890 a = {1}; Do[k = 2; While[Nand[! MemberQ[a, k], MemberQ[IntegerDigits[k], Max@ IntegerDigits[a[[n - 1]] ]]], k++]; AppendTo[a, k], {n, 2, 102}]; a (* _Michael De Vlieger_, Jul 22 2017 *)
%Y A286890 Cf. A184992.
%K A286890 nonn,base
%O A286890 1,2
%A A286890 _Enrique Navarrete_, Jul 22 2017