A307023 Lexicographically earliest sequence starting with a(1) = 1 and a(2) = 2 such that two consecutive terms of opposite parity are followed by their sum; else (same parity), by the smallest term not yet in the sequence.

1, 2, 3, 5, 4, 9, 13, 6, 19, 25, 7, 8, 15, 23, 10, 33, 43, 11, 12, 23, 35, 14, 49, 63, 16, 79, 95, 17, 18, 35, 53, 20, 73, 93, 21, 22, 43, 65, 24, 89, 113, 26, 139, 165, 27, 28, 55, 83, 29, 30, 59, 89, 31, 32, 63, 95, 34, 129, 163, 36, 199, 235, 37, 38, 75, 113, 39, 40, 79, 119, 41, 42, 83, 125, 44, 169, 213, 45, 46, 91, 137

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Mar 20 2019

Keywords

• base
• nonn
• look

Examples

			The sequence starts with 1,2,3,5,4,9,13,6,19,25,7,... and we see that:
a(1) = 1 and a(2) = 2 being of opposite parity are followed by their sum (3);
a(2) = 2 and a(3) = 3 being of opposite parity are followed by their sum (5);
a(3) = 3 and a(4) = 5 being of the same parity are followed by the smallest term not yet in the sequence (4);
a(4) = 5 and a(5) = 4 being of opposite parity are followed by their sum (9);
a(5) = 4 and a(6) = 9 being of opposite parity are followed by their sum (13);
a(6) = 9 and a(7) = 13 being of the same parity are followed by the smallest term not yet in the sequence (6);
etc.
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..10002