A006705 Solution to Pellian: y such that x^2 - n y^2 = +- 1, +- 4.
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
Offset: 1
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 (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)
Crossrefs
Cf. A006704.
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]]] = 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 *)
Extensions
3 terms corrected by Jean-François Alcover, Mar 09 2012
Extended by Ray Chandler, Aug 22 2015
Comments