%I A003285 M0018
%S A003285 0,1,2,0,1,2,4,2,0,1,2,2,5,4,2,0,1,2,6,2,6,6,4,2,0,1,2,4,5,2,8,4,4,4,2,
               0,
%T A003285 1,2,2,2,3,2,10,8,6,12,4,2,0,1,2,6,5,6,4,2,6,7,6,4,11,4,2,0,1,2,10,2,8,
               6,
%U A003285 8,2,7,5,4,12,6,4,4,2,0,1,2,2,5,10,2,6,5,2,8,8,10,16,4,4,11,4,2,0,1,2,
               12
%N A003285 Period of continued fraction for square root of n (or 0 if n is a square).
%C A003285 Any string of five consecutive terms m^2 - 2 through m^2 + 2 for m>2 
               in the sequence has the corresponding period lengths 4,2,0,1,2. - 
               Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 17 2001
%D A003285 A. Brousseau, Number Theory Tables. Fibonacci Association, San Jose, 
               CA, 1973, p. 197.
%D A003285 C. D. Patterson and H. C. Williams, "Some Periodic Continued Fractions 
               with Long Periods," Mathematics of Computation, Vol. 44 (1985), No. 
               170, pp. 523-532.
%D A003285 A. M. Rockett and P. Szuesz, On the lengths of the periods of the continued 
               fractions of square-roots of integers, Forum Mathematicum, 2 (1990), 
               119-123.
%D A003285 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003285 R. G. Stanton, C. Sudler, Jr. and H. C. Williams, "An Upper Bound for 
               the Period of the Simple Continued Fraction for Sqrt(D)," Pacific 
               Journal of Math., Vol. 67 (1976), No. 2, pp. 525-536.
%D A003285 Hanna Uscka-Wehlou, Continued Fractions and Digital Lines with Irrational 
               Slopes, in Discrete Geometry for Computer Imagery, Lecture Notes 
               in Computer Science, Volume 4992/2008, Springer-Verlag. [From N. 
               J. A. Sloane, Jul 10 2009]
%D A003285 H. C. Williams, "A Numerical Investigation Into the Length of the Period 
               of the Continued Fraction Expansion of Sqrt(D)," Mathematics of Computation, 
               Vol. 36 (1981), No. 154, pp. 593-601.
%H A003285 T. D. Noe, <a href="b003285.txt">Table of n, a(n) for n = 1..5000</a>
%H A003285 M. Beceanu, <a href="http://www.math.princeton.edu/mathlab/jr02fall/Periodicity/
               mariusjp.pdf">Period of the Continued Fraction of sqrt(n)</a>
%H A003285 Ron Knott, <a href="http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/
               cfINTRO.html#sqrts">All square-root continued fractions eventually 
               repeat</a>
%H A003285 Justin T. Miller, <a href="http://math.arizona.edu/~ura/993/miller.justin/
               ">Families of Continued Fractions</a>
%H A003285 A. J. van der Poorten, <a href="http://www-centre.mpce.mq.edu.au/alfpapers/
               a075.pdf">An introduction to continued fractions</a>
%H A003285 A. J. van der Poorten, <a href="http://www-centre.mpce.mq.edu.au/alfpapers/
               a090.pdf">Fractional parts of the period of the ...</a>
%t A003285 a[n_] := ContinuedFraction[Sqrt[n]] // If[Length[ # ] == 1, 0, Length[Last[ 
               # ]]]&
%Y A003285 Cf. A035015, A013943, A054269, A061490, A065938.
%Y A003285 Cf. A067280, A097853.
%Y A003285 Sequence in context: A144172 A166692 A046766 this_sequence A059347 A071496 
               A071502
%Y A003285 Adjacent sequences: A003282 A003283 A003284 this_sequence A003286 A003287 
               A003288
%K A003285 nonn,nice,easy
%O A003285 1,3
%A A003285 N. J. A. Sloane (njas(AT)research.att.com).