Running second maximum of a list
Husk, 9 7 bytes
Saved a byte or two thanks to @Zgarb
mȯ→hOtḣ

Returns 0 for the first &quot;second maximum&quot;
Explaination
         -- implicit input, e.g          [1,5,3,6]
      ḣ  -- prefixes                     [[],[1],[1,5],[1,5,3],[1,5,3,6]]
     t   -- remove the first element     [[1],[1,5],[1,5,3],[1,5,3,6]]
mȯ       -- map the composition of 3 functions
    O    --   sort                       [[1],[1,5],[1,3,5],[1,3,5,6]]
   h     --   drop the last element      [[],[1],[1,3],[1,3,5]
  →      --   return the last element    [0,1,3,5]
         -- implicit output

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