A Euro-iginal Sequence
Jelly, 7 bytes

b8d4ḅ5Ḍ


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How it works

b8d4ḅ5Ḍ  Main link. Argument: n (integer)

b8       Convert n from integer to base 8.
  d4     Divmod each base-8 digit by 4, mapping the digit d to [d / 4, d % 4].
    ḅ5   Convert the quotient-remainder pairs from base 5 to integer, mapping
         [d / 4, d % 4] to (d / 4 * 5 + d % 4).
         The last two steps establish the following mapping for octal digits.
             0 -&gt; [0, 0] -&gt; 0
             1 -&gt; [0, 1] -&gt; 1
             2 -&gt; [0, 2] -&gt; 2
             3 -&gt; [0, 3] -&gt; 3
             4 -&gt; [1, 0] -&gt; 5
             5 -&gt; [1, 1] -&gt; 6
             6 -&gt; [1, 2] -&gt; 7
             7 -&gt; [1, 3] -&gt; 8
      Ḍ  Convert the resulting array of digits from decimal to integer.