The Hofstadter 
-sequence
is defined by 
and
for integers 
. The first few terms for
, 2, ... are 1, 1, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9,
10, 10, 11, 12, 13, 13, 14, ... (OEIS A005374).
The generalized Hofstadter sequences include the Hofstadter G-sequence 
and 
. Letouzey (2026) proved 
for every 
, with strict inequality for 
.
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References
Hofstadter, D. R. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Vintage Books, p. 137,
1989.Letouzey, P. "Re-Ordering the Generalized Hofstadter Functions
G, H, and Beyond." 26 Oct 2026. https://arxiv.org/abs/2610.35994.Sloane,
N. J. A. Sequence A005374/M0449
in "The On-Line Encyclopedia of Integer Sequences."Referenced
on Wolfram|Alpha
Hofstadter H-Sequence
Cite this as:
Weisstein, Eric W. "Hofstadter H-Sequence."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HofstadterH-Sequence.html
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