This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A041090 #26 Jul 09 2025 00:15:25
%S A041090 7,22,29,51,182,2599,7979,10578,18557,66249,946043,2904378,3850421,
%T A041090 6754799,24114818,344362251,1057201571,1401563822,2458765393,
%U A041090 8777860001,125348805407,384824276222,510173081629,894997357851,3195165155182,45627309530399
%N A041090 Numerators of continued fraction convergents to sqrt(53).
%C A041090 The terms of this sequence can be constructed with the terms of sequence A086902. For the terms of the periodical 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 A041090 Vincenzo Librandi, <a href="/A041090/b041090.txt">Table of n, a(n) for n = 0..1000</a>
%H A041090 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,364,0,0,0,0,1).
%F A041090 a(5*n) = A086902(3*n+1), a(5*n+1) = (A086902(3*n+2)-A086902(3*n+1))/2, a(5*n+2) = (A086902(3*n+2)+A086902(3*n+1))/2, a(5*n+3) = A086902(3*n+2) and a(5*n+4) = A086902(3*n+3)/2. - _Johannes W. Meijer_, Jun 12 2010
%F A041090 G.f.: -(x^9-7*x^8+22*x^7-29*x^6+51*x^5+182*x^4+51*x^3+29*x^2+22*x+7) / (x^10+364*x^5-1). - _Colin Barker_, Sep 26 2013
%t A041090 Numerator[Convergents[Sqrt[53],30]] (* _Harvey P. Dale_, Sep 24 2013 *)
%t A041090 CoefficientList[Series[-(x^9 - 7 x^8 + 22 x^7 - 29 x^6 + 51 x^5 + 182 x^4 + 51 x^3 + 29 x^2 + 22 x + 7)/(x^10 + 364 x^5 - 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 27 2013 *)
%Y A041090 Cf. A041091, A041018, A041046, A041150, A041226, A041318, A041426 and A041550.
%K A041090 nonn,frac,easy
%O A041090 0,1
%A A041090 _N. J. A. Sloane_
%E A041090 More terms from _Colin Barker_, Sep 26 2013