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%I #17 Apr 19 2024 17:38:33
%S 1,221,12,21,2,332,23,32,3,113,31,13,4,114,41,14,5,115,51,15,6,116,61,
%T 16,7,117,71,17,8,118,81,18,9,119,91,19,10,2201,102,201,11,2211,112,
%U 211,20,3302,203,302,22,3322,223,322,24,142,241,42,25,152,251,52,26,162,261,62,27,172,271,72,28,182,281,82,29,192,291,92,30
%N The (2n-1)st pair of terms and the (2n)th pair of terms share the same palindromic digit succession. This is the lexicographically earliest sequence of distinct terms > 0 with this property.
%H Giorgos Kalogeropoulos, <a href="/A371899/b371899.txt">Table of n, a(n) for n = 1 to 9999</a>
%H Eric Angelini, <a href="https://cinquantesignes.blogspot.com/2024/04/palindromaniac.html">Palindromaniac</a>, Personal blog, April 2024.
%e The 1st pair of terms (1,221) and the 2nd one (12,21) share the same palindromic digit succession.
%e The 3rd pair of terms (2,332) and the 4th one (23,32) share the same palindromic digit succession.
%e The 5th pair of terms (3,113) and the 6th one (31,13) share the same palindromic digit succession. Etc.
%t lst={1};Do[While[f=Flatten[IntegerDigits/@{Last@lst,k}];
%t f1=First@SortBy[Select[Table[FromDigits/@TakeDrop[f,m],{m,Length@f-1}],ContainsNone[lst,#]&],First];
%t !ListQ@f1||MemberQ[lst,k]||ContainsAny[lst,f1]||Equal@@f1||!PalindromeQ@f,k++];
%t lst=Join[lst,{k},f1];k=1;While[MemberQ[lst,k],k++];AppendTo[lst,k],{w,20}];lst
%Y Cf. A371113.
%K base,nonn,look
%O 1,2
%A _Eric Angelini_ and _Giorgos Kalogeropoulos_, Apr 11 2024