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, ... (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."