cp's OEIS Frontend

A041046 Numerators of continued fraction convergents to sqrt(29).

%I A041046 #31 Jul 09 2025 00:11:35
%S A041046 5,11,16,27,70,727,1524,2251,3775,9801,101785,213371,315156,528527,
%T A041046 1372210,14250627,29873464,44124091,73997555,192119201,1995189565,
%U A041046 4182498331,6177687896,10360186227,26898060350
%N A041046 Numerators of continued fraction convergents to sqrt(29).
%C A041046 From _Johannes W. Meijer_, Jun 12 2010: (Start)
%C A041046 The terms of this sequence can be constructed with the terms of sequence A087130.
%C A041046 For the terms of the periodical sequence of the continued fraction for sqrt(29) see A010128. We observe that its period is five. The decimal expansion of sqrt(29) is A010484.  (End)
%H A041046 Vincenzo Librandi, <a href="/A041046/b041046.txt">Table of n, a(n) for n = 0..200</a>
%H A041046 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,140,0,0,0,0,1).
%F A041046 a(5*n) = A087130(3*n+1), a(5*n+1) = (A087130(3*n+2) - A087130(3*n+1))/2, a(5*n+2) = ( A087130(3*n+2) + A087130(3*n+1))/2, a(5*n+3) = A087130(3*n+2) and a(5*n+4) = A087130(3*n+3)/2. - _Johannes W. Meijer_, Jun 12 2010
%F A041046 G.f.: (5 + 11*x + 16*x^2 + 27*x^3 + 70*x^4 + 27*x^5 - 16*x^6 + 11*x^7 - 5*x^8 + x^9)/(1 - 140*x^5 - x^10) - _Peter J. C. Moses_, Jul 29 2013
%t A041046 Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[29],n]]],{n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 18 2011 *)
%t A041046 Numerator[Convergents[Sqrt[29], 30]] (* _Vincenzo Librandi_, Oct 28 2013 *)
%t A041046 LinearRecurrence[ {0,0,0,0,140,0,0,0,0,1},{5,11,16,27,70,727,1524,2251,3775,9801},30] (* _Harvey P. Dale_, Jun 10 2021 *)
%Y A041046 Cf. A041047, A041018, A041046, A041090, A041150, A041226, A041318, A041426, A041550, A010484.
%K A041046 nonn,frac,easy
%O A041046 0,1
%A A041046 _N. J. A. Sloane_