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Lexicographically earliest sequence of distinct terms such that the digits of two contiguous terms sum up to a palindrome.
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%I #16 Aug 06 2023 08:38:52

%S 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 26,68,35,77,44,86,53,95,62,100,19,39,28,48,37,57,46,66,55,75,64,84,

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

%C 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 Jean-Marc Falcoz, <a href="/A308719/b308719.txt">Table of n, a(n) for n = 1..10001</a>

%e The sequence starts with 1,2,3,4,5,6,10,7,11,9,... and we see indeed that the digits of:

%e {a(1); a(2)} have sum 1 + 2 = 3 (palindrome);

%e {a(2); a(3)} have sum 2 + 3 = 5 (palindrome);

%e {a(3); a(4)} have sum 3 + 4 = 7 (palindrome);

%e {a(4); a(5)} have sum 4 + 5 = 9 (palindrome);

%e {a(5); a(6)} have sum 5 + 6 = 11 (palindrome);

%e {a(6); a(7)} have sum 6 + 1 + 0 = 7 (palindrome);

%e {a(7); a(8)} have sum 1 + 0 + 7 = 8 (palindrome);

%e {a(8); a(9)} have sum 7 + 1 + 1 = 9 (palindrome);

%e {a(9); a(10)} have sum 1 + 1 + 9 = 11 (palindrome);

%e etc.

%t 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 Array[a,68] (* _Giorgos Kalogeropoulos_, Jul 14 2023 *)

%Y Cf. A308727 with squares instead of palindromes and A308728 with primes.

%Y Cf. A228407.

%K base,nonn

%O 1,2

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Jun 19 2019