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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.

%I A307023 #8 Mar 21 2019 17:20:39
%S A307023 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,
%T A307023 95,17,18,35,53,20,73,93,21,22,43,65,24,89,113,26,139,165,27,28,55,83,
%U A307023 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
%N 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.
%H A307023 Jean-Marc Falcoz, <a href="/A307023/b307023.txt">Table of n, a(n) for n = 1..10002</a>
%e A307023 The sequence starts with 1,2,3,5,4,9,13,6,19,25,7,... and we see that:
%e A307023 a(1) = 1 and a(2) = 2 being of opposite parity are followed by their sum (3);
%e A307023 a(2) = 2 and a(3) = 3 being of opposite parity are followed by their sum (5);
%e A307023 a(3) = 3 and a(4) = 5 being of the same parity are followed by the smallest term not yet in the sequence (4);
%e A307023 a(4) = 5 and a(5) = 4 being of opposite parity are followed by their sum (9);
%e A307023 a(5) = 4 and a(6) = 9 being of opposite parity are followed by their sum (13);
%e A307023 a(6) = 9 and a(7) = 13 being of the same parity are followed by the smallest term not yet in the sequence (6);
%e A307023 etc.
%K A307023 base,nonn,look
%O A307023 1,2
%A A307023 _Eric Angelini_ and _Jean-Marc Falcoz_, Mar 20 2019