TOPICS
Hofstadter G-Sequence
The sequence defined by 
and
 |
(1)
|
The first few terms for 
, 2, ... are 1, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 9,
... (OEIS A005206).
This can be written as a simple recurrence relation
 |
(2)
|
with 
and 
and where 
is the floor function and 
the golden ratio.
Closed forms include
 |  |  |
(3)
|
 |  |  |
(4)
|
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References
Gault, D. and Clint, M. "'Curiouser and Curiouser,' Said Alice. Further Reflections on an Interesting Recursive Function." Internat. J. Computer Math. 26, 35-43, 1988.Gould, H. W.; Kim, J. B.; and Hoggatt, V. E. Jr. "Sequences Associated with T-Ary Coding of Fibonacci's Rabbits." Fib. Quart. 15, 311-318, 1977.Granville, V. and Rasson, J. P. "A Strange Recursive Relation." J. Number Th. 30, 238-241, 1988.Grytczuk, J. "Another Variation on Conway's Recursive Sequence." Discr. Math. 282, 149-161, 2004.Hofstadter, D. R. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Vintage Books, p. 137, 1989.Sloane, N. J. A. Sequence A005206/M0436 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Hofstadter G-SequenceCite this as:
Weisstein, Eric W. "Hofstadter G-Sequence." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HofstadterG-Sequence.html