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%I M0119 #27 Oct 18 2017 02:47:10
%S 1,1,2,1,1,5,8,2,1,3,10,4,3,15,4,1,4,17,170,4,5,197,24,5,1,5,26,16,5,
%T 11,1520,6,23,35,6,1,6,37,25,6,32,13,3482,20,7,24335,48,7,1,7,50,36,7,
%U 485,89,15,151,99,530,8,39,63,8,1,8,65,48842,8,25,251,3480,17,1068,43
%N Solution to Pellian: x such that x^2 - n y^2 = +- 1, +- 4.
%C The definition of the sequence is unclear. - _Michael Somos_, Mar 07 2012
%C 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
%D 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.
%D C. F. Degen, Canon Pellianus. Hafniae, Copenhagen, 1817.
%D D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 55.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Ray Chandler, <a href="/A006704/b006704.txt">Table of n, a(n) for n = 1..10000</a>
%H A. Cayley, <a href="/A002349/a002349.pdf">Report of a committee appointed for the purpose of carrying on the tables connected with the Pellian equation ...</a>, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 13, pp. 430-443. (Annotated scanned copy)
%t 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]]] = 1; a[n_] := (x = 1; While[r[x, n] === False, x++]; x); yy[1, _] = 1; yy[x_, n_] := r[x, n][[2]]; A006704 = Table[x = a[n]; Print[{n, x, yy[x, n]}]; x, {n, 1, 55}] (* _Jean-François Alcover_, Mar 07 2012 *)
%Y Cf. A006705.
%K nonn
%O 1,3
%A _N. J. A. Sloane_.
%E 5 terms corrected by _Jean-François Alcover_, Mar 09 2012
%E Corrected a(47)=48 and extended by _Ray Chandler_, Aug 22 2015
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