An unknowably odd function
JavaScript (ES7),  33  29 bytes
This is A307485: one odd, two even, four odd, eight even, etc.
n=&gt;n-~n-(4&lt;&lt;Math.log2(n))/3|0

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For \$n\in\mathbb{N}^*\$, this is equivalent to:
$$a(n)=2n+1-\left\lceil\frac{2^{\lfloor log_2 n\rfloor+2}}{3}\right\rceil$$
It produces the sequence:
1
2 4
3 5 7 9
6 8 10 12 14 16 18 20
...

The ratio of odd values is 'bouncing' ad infinitum between \$1/3\$ and \$2/3\$, more and more slowly: