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A006703
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Solution to Pellian: y such that x^2 - n^y^2 = +-1.
(Formerly M0399)
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8
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0, 1, 1, 0, 1, 2, 3, 1, 0, 1, 3, 2, 5, 4, 1, 0, 1, 4, 39, 2, 12, 42, 5, 1, 0, 1, 5, 24, 13, 2, 273, 3, 4, 6, 1, 0, 1, 6, 4, 3, 5, 2, 531, 30, 24, 3588, 7, 1, 0, 1, 7, 90, 25, 66, 12, 2, 20, 13, 69, 4, 3805, 8, 1, 0, 1, 8, 5967, 4, 936, 30, 413, 2, 125, 5, 3, 6630, 40, 6, 9
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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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]]] = 0; a[n_] := a[n] = (k = 1; While[r[k, n] === False, k++]; y /. ToRules[r[k, n]]); Table[ Print[ a[n] ]; a[n], {n, 1, 79}] (* From Jean-François Alcover, Jan 30 2012 *)
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CROSSREFS
| Cf. A006702 (for the x values), A077233
Sequence in context: A050074 A006705 A031269 * A133623 A065862 A189117
Adjacent sequences: A006700 A006701 A006702 * A006704 A006705 A006706
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KEYWORD
| nonn
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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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