Search: id:A075870
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%I A075870
%S A075870 2,10,58,338,1970,11482,66922,390050,2273378,13250218,77227930,
%T A075870 450117362,2623476242,15290740090,89120964298,519435045698,
%U A075870 3027489309890,17645500813642,102845515571962,599427592618130
%N A075870 2*n^2 - 4 is a square.
%C A075870 Lim. n-> Inf. a(n)/a(n-1) = 3 + 2*Sqrt(2).
%C A075870 Also gives solutions to the equation x^2-2 = floor(x*r*floor(x/r)) where 
               r=sqrt(2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 14 2004
%C A075870 The upper intermediate convergents to 2^(1/2) beginning with 10/7, 58/
               41, 338/239, 1970/1393 form a strictly decreasing sequence; essentially, 
               numerators=A075870, denominators=A002315. - Clark Kimberling (ck6(AT)evansville.edu), 
               Aug 27 2008
%D A075870 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 A075870 L. E. Dickson, History of the Theory of Numbers, Vol. II, Diophantine 
               Analysis. AMS Chelsea Publishing, Providence, Rhode Island, 1999, 
               p. 341-400.
%D A075870 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 A075870 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A075870 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A075870 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 A075870 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 A075870 a(n) = 1/sqrt(2)*((1+sqrt(2))^(2*n-1)-(1-sqrt(2))^(2*n-1)) = 6*a(n-1) 
               - a(n-2)
%F A075870 G.f.: 2x(1-x)/(1-6x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 17 2008]
%Y A075870 Cf. 2*A001653.
%Y A075870 Sequence in context: A000172 A097971 A093303 this_sequence A074608 A086871 
               A108450
%Y A075870 Adjacent sequences: A075867 A075868 A075869 this_sequence A075871 A075872 
               A075873
%K A075870 nonn
%O A075870 1,1
%A A075870 Gregory V. Richardson (omomom(AT)hotmail.com), Oct 16 2002

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