The sequence defined by 
and
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The first few terms are 1, 1, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 13, 13, 14, ... (OEIS A005374).
Hofstadter H-Sequence
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References
Hofstadter, D. R. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Vintage Books, p. 137, 1989.Sloane, N. J. A. Sequence A005374/M0449 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Hofstadter H-SequenceCite this as:
Weisstein, Eric W. "Hofstadter H-Sequence." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HofstadterH-Sequence.html