

A006704


Solution to Pellian: x such that x^2  n y^2 = + 1, + 4.
(Formerly M0119)


5



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
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OFFSET

1,3


COMMENTS

The definition of the sequence is unclear.  Michael Somos, Mar 07 2012
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. 113, Cambridge Univ. Press, London, 18891897, Vol. 13, pp. 430443.
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. 113, Cambridge Univ. Press, London, 18891897, Vol. 13, pp. 430443. (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]]] = 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}] (* JeanFrançois Alcover, Mar 07 2012 *)


CROSSREFS

Cf. A006705.
Sequence in context: A024462 A049252 A098315 * A324960 A174986 A036563
Adjacent sequences: A006701 A006702 A006703 * A006705 A006706 A006707


KEYWORD

nonn


AUTHOR

N. J. A. Sloane.


EXTENSIONS

5 terms corrected by JeanFrançois Alcover, Mar 09 2012
Corrected a(47)=48 and extended by Ray Chandler, Aug 22 2015


STATUS

approved



