Here's the initial output of a Haskell program used to find them (courtesy of Bertram Felgenhauer):

    4:  \1
    6:  \\1
    7:  \\2
    8:  \\\1
    9:  \\\2
    10: \\\\1
    11: \\\\2
    12: \\\\\1
    13: \\\\\2
    14: \\\\\\1
    15: \\\\\\2
    16: \\\\\\\1
    17: \\\\\\\2
    18: \\\\\\\\1
    19: \\\\\\\\2
    20: \\\\\\\\\1
    21: \(\1 1) (1 (\2))

A few more are given in [1].

[1] https://mathoverflow.net/questions/353514/whats-the-smallest...