A307024 Lexicographically earliest sequence of different terms 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, 24, 14, 16, 17, 34, 51, 85, 18, 103, 121, 20, 141, 161, 21, 22, 44, 26, 27, 53, 28, 81, 109, 29, 30, 59, 89, 31, 32, 63, 95, 35, 36, 71, 107, 37, 38, 75, 113, 39, 40, 79, 119, 41, 42, 83, 125, 45, 46, 91, 137, 47, 48, 96, 49, 145, 50, 195, 245, 52, 297, 349, 54, 403

Offset

1,2

Comments

This sequence is a permutation of the positive integers.

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

This sequence is based on the same idea developed in A307023, but with no duplicate term: a(20) = 24 here but a(20) = 23 there.

Sequence in context: A245607 A251604 A307023 * A349493 A124653 A365642

Adjacent sequences: A307021 A307022 A307023 * A307025 A307026 A307027

Keyword

base,nonn,look

Author

Eric Angelini and Jean-Marc Falcoz, Mar 20 2019

Status

approved