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Search: id:A075873
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| A075873 |
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40*n^2 + 9 is a square. |
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+0
1
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| 0, 1, 2, 9, 40, 77, 342, 1519, 2924, 12987, 57682, 111035, 493164, 2190397, 4216406, 18727245, 83177404, 160112393, 711142146, 3158550955, 6080054528, 27004674303, 119941758886, 230881959671, 1025466481368, 4554628286713
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Lim. n-> Inf. a(n)/a(n-3) = 19 + 6*Sqrt(10). Lim. n-> Inf. a(3*k)/a(3*k-1) = (11 + 2*Sqrt(10))/9. Lim. n-> Inf. a(3*k+1)/a(3*k) = (7 + 2*Sqrt(10))/3. Lim. n-> Inf. a(3*k+2)/a(3*k+1) = (7 + 2*Sqrt(10))/3.
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REFERENCES
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A. H. Beiler, "The Pellian", ch. 22 in Recreations in the Theory of Numbers: The Queen of Mathematics Entertains. Dover, New York, New York, pp. 248-268, 1966.
L. E. Dickson, History of the Theory of Numbers, Vol. II, Diophantine Analysis. AMS Chelsea Publishing, Providence, Rhode Island, 1999, p. 341-400.
Peter G. L. Dirichlet, Lectures on Number Theory (History of Mathematics Source Series, V. 16); American Mathematical Society, Providence, Rhode Island, 1999, p. 139-147.
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LINKS
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J. J. O'Connor and E. F. Robertson, Pell's Equation
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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G.f.: x(x^5+2x^4+9x^3+2x^2+x)/(x^6-38x^3+1).
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CROSSREFS
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Cf. (A075836)/2.
Adjacent sequences: A075870 A075871 A075872 this_sequence A075874 A075875 A075876
Sequence in context: A096359 A020002 A120700 this_sequence A124722 A019066 A097070
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KEYWORD
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nonn
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AUTHOR
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Gregory V. Richardson (omomom(AT)hotmail.com), Oct 16 2002
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