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 A033317 Smallest positive integer y satisfying the Pell equation x^2 - D*y^2 = 1 for nonsquare D. 18
 2, 1, 4, 2, 3, 1, 6, 3, 2, 180, 4, 1, 8, 4, 39, 2, 12, 42, 5, 1, 10, 5, 24, 1820, 2, 273, 3, 4, 6, 1, 12, 6, 4, 3, 320, 2, 531, 30, 24, 3588, 7, 1, 14, 7, 90, 9100, 66, 12, 2, 20, 2574, 69, 4, 226153980, 8, 1, 16, 8, 5967, 4, 936, 30, 413, 2, 267000, 430, 3, 6630, 40, 6, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS D = D(n) = A000037(n). - Wolfdieter Lang, Oct 04 2015 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 Laurent Beeckmans, Squares Expressible as Sum of Consecutive Squares, Am. Math. Monthly, Volume 101, Number 5, page 442, May 1994. S. R. Finch, Class number theory [Cached copy, with permission of the author] N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references) Eric Weisstein's World of Mathematics, Pell Equation MAPLE F:= proc(d) local r, Q; uses numtheory;   Q:= cfrac(sqrt(d), 'periodic', 'quotients'):   r:= nops(Q[2]);   if r::odd then     denom(cfrac([op(Q[1]), op(Q[2]), op(Q[2][1..-2])]))   else     denom(cfrac([op(Q[1]), op(Q[2][1..-2])]));   fi end proc: map(F, remove(issqr, [\$1..100])); # Robert Israel, May 17 2015 MATHEMATICA r[n_] := Reduce[x > 0 && y > 0 && x^2 - n*y^2 == 1, {x, y}, Integers] /. C[_] -> k; sol[n_] := Catch[For[k = 0, True, k++, rn = r[n]; If[rn =!= False, Throw[rn]]]]; A033313 = Reap[For[n = 2, n <= 80, n++, If[! IntegerQ[Sqrt[n]], Sow[y /. ToRules[sol[n]]]]]][[2, 1]](* Jean-François Alcover, Apr 25 2012 *) CROSSREFS Cf. A000037, A033313 (for the x's). Sequence in context: A130584 A265911 A078458 * A183200 A326732 A305422 Adjacent sequences:  A033314 A033315 A033316 * A033318 A033319 A033320 KEYWORD nonn AUTHOR STATUS approved

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Last modified October 14 15:03 EDT 2019. Contains 328019 sequences. (Running on oeis4.)