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
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
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.
Comments