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. Sequences
A030124 and
A005228/M2629
in ``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.

© 1996-9

1999-05-25