cp's OEIS Frontend

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.

A041070 Numerators of continued fraction convergents to sqrt(42).

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%I A041070 #19 Jul 09 2025 00:13:36
%S A041070 6,13,162,337,4206,8749,109194,227137,2834838,5896813,73596594,
%T A041070 153090001,1910676606,3974443213,49603995162,103182433537,
%U A041070 1287793197606,2678768828749,33433019142594,69544807113937
%N A041070 Numerators of continued fraction convergents to sqrt(42).
%H A041070 Vincenzo Librandi, <a href="/A041070/b041070.txt">Table of n, a(n) for n = 0..100</a>
%H A041070 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,26,0,-1).
%F A041070 G.f.: -(x+1)*(x^2-7*x-6) / (x^4-26*x^2+1). - _Colin Barker_, Nov 04 2013
%t A041070 Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[42],n]]],{n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 22 2011*)
%t A041070 Numerator[Convergents[Sqrt[42], 30]] (* _Vincenzo Librandi_, Oct 29 2013 *)
%t A041070 LinearRecurrence[{0,26,0,-1},{6,13,162,337},30] (* _Harvey P. Dale_, Aug 07 2019 *)
%Y A041070 Cf. A041071, A010496.
%K A041070 nonn,cofr,frac,easy
%O A041070 0,1
%A A041070 _N. J. A. Sloane_