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 A006705 Solution to Pellian: y such that x^2 - n y^2 = +- 1, +- 4. (Formerly M0398) 5
 0, 1, 1, 0, 1, 2, 3, 1, 0, 1, 3, 1, 1, 4, 1, 0, 1, 4, 39, 1, 1, 42, 5, 1, 0, 1, 5, 3, 1, 2, 273, 1, 4, 6, 1, 0, 1, 6, 4, 1, 5, 2, 531, 3, 1, 3588, 7, 1, 0, 1, 7, 5, 1, 66, 12, 2, 20, 13, 69, 1, 5, 8, 1, 0, 1, 8, 5967, 1, 3, 30, 413, 2, 125, 5, 3, 39, 1, 6, 9, 1, 0, 1, 9, 6, 1, 1122, 3, 21, 53 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS When n is a square, the trivial solution (x,y) = (1,0) is taken; otherwise we take the least nontrivial solution that satisfies one of the four equations with +1, -1, +4 or -4. - Ray Chandler, Aug 22 2015 REFERENCES A. Cayley, Report of a committee appointed for the purpose of carrying on the tables connected with the Pellian equation ..., Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 13, pp. 430-443. C. F. Degen, Canon Pellianus. Hafniae, Copenhagen, 1817. D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 55. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Robert G. Wilson v and Ray Chandler, Table of n, a(n) for n = 1..10000 (first 150 terms from Robert G. Wilson v) A. Cayley, Report of a committee appointed for the purpose of carrying on the tables connected with the Pellian equation ..., Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 13, pp. 430-443. (Annotated scanned copy) MATHEMATICA r[x_, n_] := Reduce[lhs = x^2 - n*y^2; y > 0 && (lhs == -1 || lhs == 1 || lhs == -4 || lhs == 4), y, Integers]; a[n_ /; IntegerQ[Sqrt[n]]] = 0; xx[n_ /; IntegerQ[Sqrt[n]]] = 1; a[n_] := (x = 1; While[r[x, n] === False, x++]; xx[n] = x; y /. ToRules[r[x, n]]); A006705 = Table[yn = a[n]; Print[{n, xx[n], yn}]; yn, {n, 1, 65}] (* Jean-François Alcover, Mar 08 2012 *) CROSSREFS Cf. A006704. Sequence in context: A050074 A346688 A278313 * A031269 A006703 A133623 Adjacent sequences:  A006702 A006703 A006704 * A006706 A006707 A006708 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS 3 terms corrected by Jean-François Alcover, Mar 09 2012 Extended by Ray Chandler, Aug 22 2015 STATUS approved

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Last modified January 27 15:45 EST 2022. Contains 350607 sequences. (Running on oeis4.)