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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
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
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
KEYWORD
base,nonn,look
AUTHOR
STATUS
approved