A308728 Lexicographically earliest sequence of distinct terms such that the digits of two contiguous terms sum up to a prime.

1, 2, 3, 4, 7, 6, 5, 8, 9, 11, 10, 13, 12, 17, 14, 15, 16, 19, 18, 20, 21, 22, 25, 24, 23, 26, 27, 28, 30, 31, 34, 33, 29, 35, 32, 39, 38, 42, 41, 44, 36, 37, 43, 40, 45, 46, 49, 51, 47, 48, 50, 53, 54, 55, 52, 57, 56, 60, 58, 64, 61, 66, 65, 62, 63, 59, 69, 68, 72, 71, 74, 75, 70, 73, 67, 79, 76, 82, 81, 77, 78, 80, 83

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Jun 20 2019

Keywords

• base
• nonn

Comments

It is conjectured that this sequence is a permutation of the integers > 0.

Examples

			The sequence starts with 1,2,3,4,7,6,5,8,9,11,10,13,... and we see indeed that the digits of:
{a(1); a(2)} have sum 1 + 2 = 3 (prime);
{a(2); a(3)} have sum 2 + 3 = 5 (prime);
{a(3); a(4)} have sum 3 + 4 = 7 (prime);
{a(4); a(5)} have sum 4 + 7 = 11 (prime);
{a(5); a(6)} have sum 7 + 6 = 13 (prime);
{a(6); a(7)} have sum 6 + 5 = 11 (prime);
{a(7); a(8)} have sum 5 + 8 = 13 (prime);
{a(8); a(9)} have sum 8 + 9 = 17 (prime);
{a(9); a(10)} have sum 9 + 1 + 1 = 11 (prime);
{a(10); a(11)} have sum 1 + 1 + 1 + 0 = 3 (prime);
{a(11); a(12)} have sum 1 + 0 + 1 + 3 = 5 (prime);
etc.
		

Links

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

Crossrefs

Cf. A308719 (same idea with palindromes) and A308727 (with squares).