Somos Sequence
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-Somossequences 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 
firstbecomes nonintegral for the -Somos sequence for 
, 9, ... are17, 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. SequencesA030127,A006720/M0857,A006721/M0735,A006722/M2457,A006723/M2456in ``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.
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