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A041091 Denominators of continued fraction convergents to sqrt(53).

%I A041091 #47 Jul 09 2025 00:15:32
%S A041091 1,3,4,7,25,357,1096,1453,2549,9100,129949,398947,528896,927843,
%T A041091 3312425,47301793,145217804,192519597,337737401,1205731800,
%U A041091 17217982601,52859679603,70077662204,122937341807,438889687625,6267392968557,19241068593296,25508461561853
%N A041091 Denominators of continued fraction convergents to sqrt(53).
%C A041091 The terms of this sequence can be constructed with the terms of sequence A054413. For the terms of the periodic sequence of the continued fraction for sqrt(53) see A010139. We observe that its period is five. The decimal expansion of sqrt(53) is A010506. - _Johannes W. Meijer_, Jun 12 2010
%H A041091 Vincenzo Librandi, <a href="/A041091/b041091.txt">Table of n, a(n) for n = 0..200</a>
%H A041091 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,364,0,0,0,0,1).
%F A041091 a(5*n) = A054413(3*n), a(5*n+1) = (A054413(3*n+1) - A054413(3*n))/2, a(5*n+2)= (A054413(3*n+1) + A054413(3*n))/2, a(5*n+3) = A054413(3*n+1) and a(5*n+4) = A054413(3*n+2)/2. - _Johannes W. Meijer_, Jun 12 2010
%F A041091 G.f.: -(x^8-3*x^7+4*x^6-7*x^5+25*x^4+7*x^3+4*x^2+3*x+1) / (x^10+364*x^5-1). - _Colin Barker_, Sep 26 2013
%p A041091 convert(sqrt(53), confrac, 30, cvgts): denom(cvgts); # _Wesley Ivan Hurt_, Dec 17 2013
%t A041091 Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[53], n]]], {n, 1, 50}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 23 2011 *)
%t A041091 Denominator[Convergents[Sqrt[53], 30]] (* _Vincenzo Librandi_, Oct 24 2013 *)
%t A041091 LinearRecurrence[{0,0,0,0,364,0,0,0,0,1},{1,3,4,7,25,357,1096,1453,2549,9100},30] (* _Harvey P. Dale_, Nov 13 2019 *)
%Y A041091 Cf. A010506, A041090.
%Y A041091 Cf. A041019, A041047, A041151, A041227, A041319, A041427 and A041551. - _Johannes W. Meijer_, Jun 12 2010
%K A041091 nonn,frac,easy
%O A041091 0,2
%A A041091 _N. J. A. Sloane_