A326315 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.

1, 2, 3, 4, 5, 6, 196, 197, 277, 15, 187, 105, 97, 24, 20, 13, 31, 70, 101, 10, 12, 21, 23, 98, 104, 188, 14, 30, 71, 100, 11, 22, 99, 103, 189, 285, 7, 195, 198, 276, 16, 186, 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

Offset

1,2

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..10001

Example

The sequence starts with 1,2,3,4,5,6,196,197,... and we see indeed that:
the digits of {a(1); a(2)} have sum 1 + 2 = 3 (palindrome) and a(1) + a(2) is a palindrome too (3);
the digits of {a(2); a(3)} have sum 2 + 3 = 5 (palindrome) and a(2) + a(3) is a palindrome too (5);
the digits of {a(3); a(4)} have sum 3 + 4 = 7 (palindrome) and a(3) + a(4) is a palindrome too (7);
the digits of {a(4); a(5)} have sum 4 + 5 = 9 (palindrome) and a(4) + a(5) is a palindrome too (9);
the digits of {a(5); a(6)} have sum 5 + 6 = 11 (palindrome) and a(5) + a(6) is a palindrome too (11);
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);
the digits of {a(7); a(8)} have sum 1 + 0 + 7 = 8 (palindrome) and a(7) + a(8) =  is a palindrome too (3);
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);
etc.

Crossrefs

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.

Sequence in context: A099145 A004868 A073788 * A004879 A062943 A004890

Adjacent sequences: A326312 A326313 A326314 * A326316 A326317 A326318

Keyword

base,nonn,look

Author

Eric Angelini and Jean-Marc Falcoz, Jun 24 2019

Status

approved