Hofstadter Figure-Figure Sequence
Define 
and 
and write
where the sequence ![<span style=]()
{S(n)}" src="https://mathworld.wolfram.com/images/equations/HofstadterFigure-FigureSequence/Inline3.gif" style="height:15px; width:36px" /> consists of those integers not already contained in ![<span style=]()
{F(n)}" src="https://mathworld.wolfram.com/images/equations/HofstadterFigure-FigureSequence/Inline4.gif" style="height:15px; width:38px" />. 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, ... (OEIS A005228) and the "space" sequence as 2, 4, 5, 6, 8, 9, 10, 11, 13, 14, ... (OEIS A030124).
REFERENCES:
Hofstadter, D. R. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Vintage Books, p. 73, 1989.
Sloane, N. J. A. Sequences A005228/M2629 and A030124 in "The On-Line Encyclopedia of Integer Sequences."
