cp's OEIS Frontend

A041551 Denominators of continued fraction convergents to sqrt(293).

%I A041551 #28 Jul 09 2025 01:00:53
%S A041551 1,8,9,17,145,4947,39721,44668,84389,719780,24556909,197175052,
%T A041551 221731961,418907013,3572988065,121900501223,978776997849,
%U A041551 1100677499072,2079454496921,17736313474440,605114112627881,4858649214497488,5463763327125369,10322412541622857
%N A041551 Denominators of continued fraction convergents to sqrt(293).
%C A041551 The a(n) terms of this sequence can be constructed with the terms of sequence A178765. For the terms of the periodical sequence of the continued fraction for sqrt(293) see A040275. We observe that its period is five. - _Johannes W. Meijer_, Jun 12 2010
%H A041551 Vincenzo Librandi, <a href="/A041551/b041551.txt">Table of n, a(n) for n = 0..200</a>
%H A041551 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 4964, 0, 0, 0, 0, 1).
%F A041551 a(5n) = A178765(3n), a(5n+1) = (A178765(3n+1) - A178765(3n))/2, a(5n+2) = (A178765(3n+1) + A178765(3n))/2, a(5n+3) = A178765(3n+1) and a(5n+4) = A178765(3n+2)/2. - _Johannes W. Meijer_, Jun 12 2010
%F A041551 G.f.: -(x^8-8*x^7+9*x^6-17*x^5+145*x^4+17*x^3+9*x^2+8*x+1) / (x^10+4964*x^5-1). - _Colin Barker_, Nov 12 2013
%F A041551 a(n) = 4964*a(n-5) + a(n-10) for n>9. - _Vincenzo Librandi_, Dec 20 2013
%t A041551 Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[293], n]]], {n, 1, 50}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 23 2011 *)
%t A041551 Denominator[Convergents[Sqrt[293 ], 30]] (* _Vincenzo Librandi_, Dec 20 2013 *)
%o A041551 (Magma) I:=[1,8,9,17,145,4947,39721,44668,84389,719780]; [n le 10 select I[n] else 4964*Self(n-5)+Self(n-10): n in [1..40]]; // _Vincenzo Librandi_, Dec 20 2013
%Y A041551 Cf. A041550, A040275, A041019, A041047, A041091, A041151, A041227, A041319, A041427 and A041551.
%K A041551 nonn,frac,easy
%O A041551 0,2
%A A041551 _N. J. A. Sloane_