Search: id:A075873
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%I A075873
%S A075873 0,1,2,9,40,77,342,1519,2924,12987,57682,111035,493164,2190397,4216406,
%T A075873 18727245,83177404,160112393,711142146,3158550955,6080054528,
%U A075873 27004674303,119941758886,230881959671,1025466481368,4554628286713
%N A075873 40*n^2 + 9 is a square.
%C A075873 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.
%D A075873 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.
%D A075873 L. E. Dickson, History of the Theory of Numbers, Vol. II, Diophantine 
               Analysis. AMS Chelsea Publishing, Providence, Rhode Island, 1999, 
               p. 341-400.
%D A075873 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.
%H A075873 J. J. O'Connor and E. F. Robertson, <a href="http://www-gap.dcs.st-and.ac.uk/
               ~history/HistTopics/Pell.html">Pell's Equation</a>
%H A075873 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PellEquation.html">Link to a section of The World of Mathematics.</
               a>
%F A075873 G.f.: x(x^5+2x^4+9x^3+2x^2+x)/(x^6-38x^3+1).
%Y A075873 Cf. (A075836)/2.
%Y A075873 Sequence in context: A096359 A020002 A120700 this_sequence A124722 A019066 
               A097070
%Y A075873 Adjacent sequences: A075870 A075871 A075872 this_sequence A075874 A075875 
               A075876
%K A075873 nonn
%O A075873 1,3
%A A075873 Gregory V. Richardson (omomom(AT)hotmail.com), Oct 16 2002

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