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

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

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Jun 19 2019

Keywords

• base
• nonn

Comments

This sequence is not a permutation of the integers > 0 as integers with digitsum 11, or 22, or 33, for instance, will not show.

Examples

			The sequence starts with 1,2,3,4,5,6,10,7,11,9,... and we see indeed that the digits of:
{a(1); a(2)} have sum 1 + 2 = 3 (palindrome);
{a(2); a(3)} have sum 2 + 3 = 5 (palindrome);
{a(3); a(4)} have sum 3 + 4 = 7 (palindrome);
{a(4); a(5)} have sum 4 + 5 = 9 (palindrome);
{a(5); a(6)} have sum 5 + 6 = 11 (palindrome);
{a(6); a(7)} have sum 6 + 1 + 0 = 7 (palindrome);
{a(7); a(8)} have sum 1 + 0 + 7 = 8 (palindrome);
{a(8); a(9)} have sum 7 + 1 + 1 = 9 (palindrome);
{a(9); a(10)} have sum 1 + 1 + 9 = 11 (palindrome);
etc.
		

Links

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

Crossrefs

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

Cf. A228407.

Programs

Mathematica

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)
Array[a,68] (* Giorgos Kalogeropoulos, Jul 14 2023 *)