Search: id:A033314
Results 1-1 of 1 results found.

%I A033314
%S A033314 3,2,15,6,35,12,7,5,11,30,143,42,195,14,255,18,323,10,399,110,483,33,
%T A033314 23,39,27,182,87,210,899,60,1023,17,1155,34,1295,38,1443,95,1599,105,
%U A033314 1763,462,215,506,235,138,47,96,51,26,2703,78,2915,21,3135,203,3363
%N A033314 Least D in the Pellian x^2 - D*y^2 = 1 for which x has least solution 
               n.
%C A033314 The i-th solution pair V(i) = [x(i), y(i)] to the Pellian x^2 - D*y^2 
               = 1 for a given least solution x(1) = n may be generated through 
               the recurrence V(i+2) = 2*n*V(i+1) - V(i) taking V(0) = [1, 0] and 
               V(1) = [n, sqrt{(n^2-1)/a(n)}]. V(i) stands for the numerator and 
               denominator of the 2i-th convergent of the continued fraction expansion 
               of sqrt(D).
%C A033314 Thus setting n = 3, for instance, we have D = a(3) = 2 and V(1) = [3, 
               2] so that along with V(0) = [1, 0] recurrence V(i+2) = 6*V(i+1)-V(i) 
               generates [A001333(2k), A000129(2k)]. Similarly, setting n = 9 generates 
               [A023039, A060645], respectively the numerator and denominator of 
               the 2i-th convergent of sqrt{a(9)}, i.e. sqrt{5}. - Lekraj Beedassy 
               (blekraj(AT)yahoo.com), Feb 26 2002
%H A033314 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PellEquation.html">Link to a section of The World of Mathematics.</
               a>
%Y A033314 Cf. A033313.
%Y A033314 Sequence in context: A055234 A086485 A068310 this_sequence A070260 A142705 
               A072346
%Y A033314 Adjacent sequences: A033311 A033312 A033313 this_sequence A033315 A033316 
               A033317
%K A033314 nonn
%O A033314 2,1
%A A033314 Eric Weisstein (eric(AT)weisstein.com)

Search completed in 0.001 seconds