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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-Fran├žois Alcover, Apr 25 2012 *)

CROSSREFS

Cf. A000037, A033313 (for the x's).

Sequence in context: A130584 A265911 A078458 * A183200 A305422 A007733

Adjacent sequences:  A033314 A033315 A033316 * A033318 A033319 A033320

KEYWORD

nonn

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified June 26 10:12 EDT 2019. Contains 324375 sequences. (Running on oeis4.)