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).

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."

CITE THIS AS:

Weisstein, Eric W. "Hofstadter Figure-Figure Sequence." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/HofstadterFigure-FigureSequence.html