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.

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

Author

Eric Angelini and Jean-Marc Falcoz, Jun 24 2019

Keywords

• base
• nonn

Examples

			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.
		

Links

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

Crossrefs

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.