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A308719 Lexicographically earliest sequence of distinct terms such that the digits of two contiguous terms sum up to a palindrome.

%I A308719 #16 Aug 06 2023 08:38:52
%S A308719 1,2,3,4,5,6,10,7,11,9,20,12,8,21,13,14,15,23,22,16,31,25,40,30,17,59,
%T A308719 26,68,35,77,44,86,53,95,62,100,19,39,28,48,37,57,46,66,55,75,64,84,
%U A308719 73,93,82,129,91,138,109,147,118,156,127,165,136,174,145,183,154,192,163,219,172,228,181,237,190
%N A308719 Lexicographically earliest sequence of distinct terms such that the digits of two contiguous terms sum up to a palindrome.
%C A308719 This sequence is not a permutation of the integers > 0 as integers with digitsum 11, or 22, or 33, for instance, will not show.
%H A308719 Jean-Marc Falcoz, <a href="/A308719/b308719.txt">Table of n, a(n) for n = 1..10001</a>
%e A308719 The sequence starts with 1,2,3,4,5,6,10,7,11,9,... and we see indeed that the digits of:
%e A308719 {a(1); a(2)} have sum 1 + 2 = 3 (palindrome);
%e A308719 {a(2); a(3)} have sum 2 + 3 = 5 (palindrome);
%e A308719 {a(3); a(4)} have sum 3 + 4 = 7 (palindrome);
%e A308719 {a(4); a(5)} have sum 4 + 5 = 9 (palindrome);
%e A308719 {a(5); a(6)} have sum 5 + 6 = 11 (palindrome);
%e A308719 {a(6); a(7)} have sum 6 + 1 + 0 = 7 (palindrome);
%e A308719 {a(7); a(8)} have sum 1 + 0 + 7 = 8 (palindrome);
%e A308719 {a(8); a(9)} have sum 7 + 1 + 1 = 9 (palindrome);
%e A308719 {a(9); a(10)} have sum 1 + 1 + 9 = 11 (palindrome);
%e A308719 etc.
%t A308719 a[1]=1; a[n_]:=a[n]=(k=1;While[MemberQ[Array[a,n-1],k]|| !PalindromeQ@Total[Join[IntegerDigits@a[n-1],IntegerDigits@k]], k++];k)
%t A308719 Array[a,68] (* _Giorgos Kalogeropoulos_, Jul 14 2023 *)
%Y A308719 Cf. A308727 with squares instead of palindromes and A308728 with primes.
%Y A308719 Cf. A228407.
%K A308719 base,nonn
%O A308719 1,2
%A A308719 _Eric Angelini_ and _Jean-Marc Falcoz_, Jun 19 2019