The Somos sequences are a set of related symmetrical Recurrence Relations which,
surprisingly, always give integers. The Somos sequence of order is defined by

where is the Floor Function and for , ..., . The 2- and 3-Somos sequences consist entirely of 1s. The -Somos sequences for , 5, 6, and 7 are

However, the -Somos sequences for do not give integers. The values of for which first becomes nonintegral for the -Somos sequence for , 9, ... are 17, 19, 20, 22, 24, 27, 28, 30, 33, 34, 36, 39, 41, 42, 44, 46, 48, 51, 52, 55, 56, 58, 60, ... (Sloane's A030127).

**References**

Buchholz, R. H. and Rathbun, R. L. ``An Infinite Set of Heron Triangles with Two Rational Medians.''
*Amer. Math. Monthly* **104**, 107-115, 1997.

Gale, D. ``Mathematical Entertainments: The Strange and Surprising Saga of the
Somos Sequences.'' *Math. Intel.* **13**, 40-42, 1991.

Sloane, N. J. A. Sequences
A030127,
A006720/M0857,
A006721/M0735,
A006722/M2457,
A006723/M2456
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

1999-05-26