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Numerators of continued fraction convergents to sqrt(23).
2

%I #30 Jun 13 2015 00:49:21

%S 4,5,19,24,211,235,916,1151,10124,11275,43949,55224,485741,540965,

%T 2108636,2649601,23305444,25955045,101170579,127125624,1118175571,

%U 1245301195,4854079156,6099380351,53649121964

%N Numerators of continued fraction convergents to sqrt(23).

%H Vincenzo Librandi, <a href="/A041036/b041036.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,48,0,0,0,-1).

%F G.f.: (4+5*x+19*x^2+24*x^3+19*x^4-5*x^5+4*x^6-x^7)/(1-48*x^4+x^8). [_Colin Barker_, Jan 03 2012]

%t Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[23],n]]],{n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 17 2011 *)

%t Numerator[Convergents[Sqrt[23],40]] (* _Harvey P. Dale_, Nov 29 2012 *)

%Y Cf. A010479, A041037.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.