A326315 - OEIS

%I #13 Jun 25 2019 22:23:25

%S 1,2,3,4,5,6,196,197,277,15,187,105,97,24,20,13,31,70,101,10,12,21,23,

%T 98,104,188,14,30,71,100,11,22,99,103,189,285,7,195,198,276,16,186,

%U 106,96,25,177,115,87,34,168,124,78,43,159,133,69,52,200,32,89,113,179,295,240,376,411,457,330,286,269,367,420,448,501

%N Lexicographically earliest sequence of distinct terms such that the digits of a(n) and a(n+1) sum up to a palindrome and a(n) + a(n+1) is also a palindrome.

%H Jean-Marc Falcoz, <a href="/A326315/b326315.txt">Table of n, a(n) for n = 1..10001</a>

%e The sequence starts with 1,2,3,4,5,6,196,197,... and we see indeed that:

%e the digits of {a(1); a(2)} have sum 1 + 2 = 3 (palindrome) and a(1) + a(2) is a palindrome too (3);

%e the digits of {a(2); a(3)} have sum 2 + 3 = 5 (palindrome) and a(2) + a(3) is a palindrome too (5);

%e the digits of {a(3); a(4)} have sum 3 + 4 = 7 (palindrome) and a(3) + a(4) is a palindrome too (7);

%e the digits of {a(4); a(5)} have sum 4 + 5 = 9 (palindrome) and a(4) + a(5) is a palindrome too (9);

%e the digits of {a(5); a(6)} have sum 5 + 6 = 11 (palindrome) and a(5) + a(6) is a palindrome too (11);

%e the digits of {a(6); a(7)} have sum 6 + 1 + 9 + 6 = 22 (palindrome) and a(6) + a(7) = 6 + 196 is a palindrome too (202);

%e the digits of {a(7); a(8)} have sum 1 + 0 + 7 = 8 (palindrome) and a(7) + a(8) =  is a palindrome too (3);

%e the digits of {a(8); a(9)} have sum 1 + 9 + 6 + 1 + 9 + 7 = 33 (palindrome) and a(8) + a(9) = 196 + 197 is a palindrome too (393);

%e etc.

%Y Cf. A326316 (replace the word "palindrome" by "prime"), A326317 (replace the word "palindrome" by "square"); in A308719 only the sum of the digits is a palindrome.

%K base,nonn,look

%O 1,2

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Jun 24 2019