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A006702
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Solution to a Pellian equation: least x such that x^2 - n y^2 = +- 1.
(Formerly M0120)
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8
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1, 1, 2, 1, 2, 5, 8, 3, 1, 3, 10, 7, 18, 15, 4, 1, 4, 17, 170, 9, 55, 197, 24, 5, 1, 5, 26, 127, 70, 11, 1520, 17, 23, 35, 6, 1, 6, 37, 25, 19, 32, 13, 3482, 199, 161, 24335, 48, 7, 1, 7, 50, 649, 182, 485, 89, 15, 151, 99, 530, 31, 29718, 63, 8, 1, 8, 65, 48842
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| When n is a square, the trivial solution x=1, y=0 is taken; otherwise we take the least x that satisfies either the +1 or -1 equation. - T. D. Noe, May 19 2007
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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).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
M. Zuker, Fundamental solution to Pell's Equation x^2 - d*y^2 = +-1
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MATHEMATICA
| r[x_, n_] := Reduce[y > 0 && (x^2 - n*y^2 == -1 || x^2 - n*y^2 == 1 ), y, Integers]; a[n_ /; IntegerQ[ Sqrt[n]]] = 1; a[n_] := a[n] = (k = 1; While[ r[k, n] === False, k++]; k); Table[ Print[ a[n] ]; a[n], {n, 1, 67}] (* From Jean-François Alcover, Jan 30 2012 *)
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CROSSREFS
| Cf. A006703, A077232
Sequence in context: A153910 A052532 A006704 * A129394 A199599 A201163
Adjacent sequences: A006699 A006700 A006701 * A006703 A006704 A006705
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Corrected and extended by T. D. Noe, May 19 2007
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