[seqfan] From Ali Sada : Another permutation of the positive integers

[Olivier Gerard]

(due to a technical glitch, I forward it myself to the list, please answer
directly to Ali Sada if your response is not fit for the list. The Admin)

Hi everyone,

We start by putting odd numbers in an ordered list and even numbers in
another. Terms in each list aim at taking out terms from the other list.
We start with the smallest number, 1. Since it can’t eliminate even numbers
on its own, we add the next smallest odd number, 3. Both of them take out
4. So, the first three terms of our sequence are 1,3,4.

Now, the smallest number in both lists is 2. On its own, it can’t take out
any number from the other list, so we add it to the next smallest number on
the even list, 6, and we get 8. There is no combination of odd numbers at
this point that adds up to 8, so we add the next smallest even number, 8,
and we get 16. 16 takes out 5 and 11. We add these five numbers to the
sequence (in order). The sequence now is 1,3,4,2,6,8,5,11.

The smallest remaining number is 7. We add it to 9 and we get 16. There is
no combination of the remaining even numbers that adds up to 16, so we
continue by adding 13 and 15 to get 44, which takes out 10 and 34. The
sequence now is 1,3,4,2,6,8,5,11,7,9,13,15,10,34.
And so on.
The first 45 terms of the sequence are
1,3,4,2,6,8,5,11,7,9,13,15,10,34,12,14,16,17,25,18,20,22,19,41,21,23,27,29,24,76,26,28,30,31,53,32,36,33,35,37,39,43,45,38,126

If this sequence is fit for the OEIS, I would appreciate any help with the
definition.

Best,

Ali