A006704 Solution to Pellian: x such that x^2 - n y^2 = +- 1, +- 4.
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, 11, 1520, 6, 23, 35, 6, 1, 6, 37, 25, 6, 32, 13, 3482, 20, 7, 24335, 48, 7, 1, 7, 50, 36, 7, 485, 89, 15, 151, 99, 530, 8, 39, 63, 8, 1, 8, 65, 48842, 8, 25, 251, 3480, 17, 1068, 43
Offset: 1
Keywords
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
- Ray Chandler, Table of n, a(n) for n = 1..10000
- 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)
Crossrefs
Cf. A006705.
Programs
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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]]] = 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 *)
Extensions
5 terms corrected by Jean-François Alcover, Mar 09 2012
Corrected a(47)=48 and extended by Ray Chandler, Aug 22 2015
Comments