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Background
This challenge is about A004001, a.k.a. Hofstadter-Conway $10000 sequence:
$$
a_1 = a_2 = 1, \quad a_n = a_{a_{n-1}} + a_{n-a_{n-1}}
$$
which starts with
1, 1, 2, 2, 3, 4, 4, 4, 5, 6, 7, 7, 8, 8, 8, 8, 9, 10, 11, 12, 12, 13, 14, 14, 15, 15, 15, 16, 16, 16, 16, 16, ...
John Conway...