A307024 - OEIS

%I #7 Mar 21 2019 17:20:46

%S 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,

%T 18,103,121,20,141,161,21,22,44,26,27,53,28,81,109,29,30,59,89,31,32,

%U 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

%N 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.

%C This sequence is a permutation of the positive integers.

%H Jean-Marc Falcoz, <a href="/A307024/b307024.txt">Table of n, a(n) for n = 1..10002</a>

%e The sequence starts with 1,2,3,5,4,9,13,6,19,25,7,... and we see that:

%e a(1) = 1 and a(2) = 2 being of opposite parity are followed by their sum (3);

%e a(2) = 2 and a(3) = 3 being of opposite parity are followed by their sum (5);

%e 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 a(4) = 5 and a(5) = 4 being of opposite parity are followed by their sum (9);

%e a(5) = 4 and a(6) = 9 being of opposite parity are followed by their sum (13);

%e 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 etc.

%Y 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.

%K base,nonn,look

%O 1,2

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Mar 20 2019