

A033314


Least D in the Pellian x^2  D*y^2 = 1 for which x has least solution n.


6



3, 2, 15, 6, 35, 12, 7, 5, 11, 30, 143, 42, 195, 14, 255, 18, 323, 10, 399, 110, 483, 33, 23, 39, 27, 182, 87, 210, 899, 60, 1023, 17, 1155, 34, 1295, 38, 1443, 95, 1599, 105, 1763, 462, 215, 506, 235, 138, 47, 96, 51, 26, 2703, 78, 2915, 21, 3135, 203, 3363
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OFFSET

2,1


COMMENTS

The ith 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^21)/a(n)}]. V(i) stands for the numerator and denominator of the 2ith convergent of the continued fraction expansion of sqrt(D).
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 2ith convergent of sqrt{a(9)}, i.e. sqrt{5}.  Lekraj Beedassy, Feb 26 2002


LINKS

Ray Chandler, Table of n, a(n) for n = 2..1001
Eric Weisstein's World of Mathematics, Pell Equation.


CROSSREFS

Cf. A000037, A033313.
Sequence in context: A328282 A086485 A068310 * A070260 A142705 A072346
Adjacent sequences: A033311 A033312 A033313 * A033315 A033316 A033317


KEYWORD

nonn


AUTHOR

Eric W. Weisstein


STATUS

approved



