Calculate the nth term of Golomb's self-describing sequence
Jelly, non-competing

10 bytes This answer is non-competing, since the challenge predates the creation of Jelly.

’ßßạ¹ß‘µṖ¡


This uses the recursive formula a(1) = 1, a(n + 1) = 1 + a(n + 1 - a(a(n))) from the OEIS page.

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How it works

’ßßạ¹ß‘µṖ¡ Main link. Input: n

’          Decrement; yield n - 1.
 ßß        Recursively call the main link twice, with argument n - 1.
   ạ¹      Take the absolute difference of a(a(n - 1)) and n.
     ß     Recursively call the main link, with argument n - a(a(n - 1)).
      ‘    Increment the result, yielding 1 + a(n - a(a(n - 1))).
       µ   Combine the chain to the left into a single link.
        Ṗ  Pop [1, ..., n]. This yields [] iff n == 1.
         ¡ Execute the chain iff Ṗ returned a non-empty array.