Hofstadter Figure-Figure Sequence
Define 
and 
and write
where the sequence
consists of those integers not already contained in 
. For example,
, so the next term of 
is 
, giving 
. The next integer is 5, so 
and 
. Continuing in this manner gives the ``figure'' sequence 
as 1, 3, 7, 12, 18, 26, 35, 45,56, ... (Sloane's A005228) and the ``space'' sequence as 2, 4, 5, 6, 8, 9, 10, 11, 13, 14, ... (Sloane's A030124).
References
Hofstadter, D. R. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Vintage Books, p. 73, 1989. Sloane, N. J. A. SequencesA030124 andA005228/M2629in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.
- Fundamental Theorem of Algebra
- Fundamental Theorem of Arithmetic
- Fundamental Theorem of Curves
- Fundamental Theorem of Directly Similar Figures
- Fundamental Theorem of Gaussian Quadrature
- Fundamental Theorem of Genera
- Fundamental Theorem of Plane Curves
- Fundamental Theorem of Projective Geometry
- Fundamental Theorem of Space Curves
- Fundamental Theorem of Symmetric Functions
- Fundamental Theorems of Calculus
- Fundamental Unit
- Funnel
- Fuss's Problem
- Futile Game
- Fuzzy Logic
- FWHM
- Gabriel's Horn
- Gabriel's Staircase
- Gadget
- Gale-Ryser Theorem
- Galilean Transformation
- Gallows
- Gall's Stereographic Projection
- Gallucci's Theorem