A308728 -id:A308728 - cp's OEIS frontend

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

Eric Angelini and Jean-Marc Falcoz, Jun 19 2019

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

			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.

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

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

Cf. A228407.

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 *)

A326316 Lexicographically earliest sequence of distinct terms such that the digits of a(n) and a(n+1) sum up to a prime and a(n) + a(n+1) is also a prime.

Original entry on oeis.org

1, 2, 3, 4, 7, 6, 5, 8, 9, 20, 21, 22, 25, 28, 43, 24, 23, 44, 27, 26, 41, 42, 29, 60, 47, 62, 45, 64, 49, 40, 61, 46, 63, 68, 69, 80, 83, 48, 65, 66, 113, 84, 89, 110, 81, 82, 67, 112, 85, 88, 111, 86, 87, 152, 117, 116, 135, 134, 137, 114, 115, 118, 133, 130, 139, 132, 119, 138, 131, 150, 157, 136, 171, 176, 177, 170

Offset: 1

Eric Angelini and Jean-Marc Falcoz, Jun 24 2019

			The sequence starts with 1,2,3,4,7,6,5,8,9,20,21,... and we see indeed that:
the digits of {a(1); a(2)} have sum 1 + 2 = 3 (prime) and a(1) + a(2) is a prime too (3);
the digits of {a(2); a(3)} have sum 2 + 3 = 5 (prime) and a(2) + a(3) is a prime too (5);
the digits of {a(3); a(4)} have sum 3 + 4 = 7 (prime) and a(3) + a(4) is a prime too (7);
the digits of {a(4); a(5)} have sum 4 + 7 = 11 (prime) and a(4) + a(5) is a prime too (11);
the digits of {a(5); a(6)} have sum 7 + 6 = 13 (prime) and a(5) + a(6) is a prime too (13);
...
the digits of {a(9); a(10)} have sum 9 + 2 + 0 = 11 (prime) and a(9) + a(10) = 9 + 20 is a prime too (29);
the digits of {a(10); a(11)} have sum 2 + 0 + 2 + 1 = 5 (prime) and a(10) + a(11) = 20 + 21 is a prime too (41);
etc.

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

Cf. A326315 (replace the word "prime" by "palindrome"), A326317 (replace the word "prime" by "square"); in A308728 only the sum of the digits is a prime.

cp's OEIS Frontend

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

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