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

1,2

Links

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

Example

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.

Crossrefs

Sequence in context: A329811 A245607 A251604 * A307024 A349493 A124653

Adjacent sequences: A307020 A307021 A307022 * A307024 A307025 A307026

Keyword

base,nonn,look

Author

Eric Angelini and Jean-Marc Falcoz, Mar 20 2019

Status

approved