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Hofstadter[1] = Hofstadter[2] = 1;
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Hofstadter[n_Integer?Positive] := Hofstadter[n] = Block[{$RecursionLimit = Infinity},
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Hofstadter[n - Hofstadter[n - 1]] + Hofstadter[n - Hofstadter[n - 2]]
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]
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Hofstadter /@ Range[10]
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{1,1,2,3,3,4,5,5,6,6}
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Hofstadter[1000]
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502
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Count[Differences[Hofstadter /@ Range[100000]], _?Negative]
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49798
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