Two interwoven chains
Python, 46 42 37 bytes

5 bytes saved thanks to @notjagan



lambda x:1&lt;x&lt;4and x*2%5or x-(x&amp;2)*4+4


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Iterates the even and odd numbers with steps of 4 and links on 2 and 3:

=&gt; 22 =&gt; 18 =&gt; 14 =&gt; 10 =&gt; 6 =&gt; 2 =&gt; 4 =&gt; 8 =&gt; 12 =&gt; 16 =&gt; 20 =&gt; 24 =&gt;
=&gt; 23 =&gt; 19 =&gt; 15 =&gt; 11 =&gt; 7 =&gt; 3 =&gt; 1 =&gt; 5 =&gt; 9 =&gt; 13 =&gt; 17 =&gt; 21 =&gt;