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 A041150 #22 Jul 09 2025 00:20:36 %S A041150 9,37,46,83,378,6887,27926,34813,62739,285769,5206581,21112093, %T A041150 26318674,47430767,216041742,3936182123,15960770234,19896952357, %U A041150 35857722591,163327842721,2975758891569,12066363408997 %N A041150 Numerators of continued fraction convergents to sqrt(85). %C A041150 From _Johannes W. Meijer_, Jun 17 2010: (Start) %C A041150 The a(n) terms of this sequence can be constructed with the terms of sequence A087798. %C A041150 For the terms of the periodic sequence of the continued fraction for sqrt(85) see A010158. We observe that its period is five. The decimal expansion of sqrt(85) is A010536. (End) %H A041150 Vincenzo Librandi, <a href="/A041150/b041150.txt">Table of n, a(n) for n = 0..200</a> %H A041150 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,756,0,0,0,0,1). %F A041150 From _Johannes W. Meijer_, Jun 17 2010: (Start) %F A041150 a(5*n) = A087798(3*n+1), a(5*n+1) = (A087798(3*n+2) - A087798(3*n+1))/2, a(5*n+2) = (A087798(3*n+2) + A087798(3*n+1))/2, a(5*n+3) = A087798(3*n+2) and a(5*n+4) = A087798(3*n+3)/2. (End) %F A041150 G.f.: -(x^9-9*x^8+37*x^7-46*x^6+83*x^5+378*x^4+83*x^3+46*x^2+37*x+9) / (x^10+756*x^5-1). - _Colin Barker_, Nov 04 2013 %t A041150 Numerator[Convergents[Sqrt[85], 30]] (* _Vincenzo Librandi_, Oct 29 2013 *) %Y A041150 Cf. A010536, A041018, A041046, A041090, A041150, A041151, A041226, A041318, A041426, %Y A041150 A041550. %K A041150 nonn,frac,easy %O A041150 0,1 %A A041150 _N. J. A. Sloane_