A320640 - OEIS

%I #20 Aug 10 2024 16:22:35

%S 1,1,1,3,1,4,1,1,3,1,1,1,7,3,8,3,3,6,1,1,1,3,10,3,1,1,1,4,4,8,6,33,8,

%T 1,4,2,2,2,38,14,2,1,1,2,1,3,18,1,10,1,23,4,2,2,4,5,4,1,1,1,3,1,1,13,

%U 1,1,3,2,1,6,2,1,1,5,16,15,2,1,4,6,120,1,1,1

%N Continued fraction of (C + sqrt(4 + C^2))/2, where C is the Catalan constant.

%C Continued fraction of the constant in A320639.

%H G. C. Greubel, <a href="/A320640/b320640.txt">Table of n, a(n) for n = 0..9999</a>

%p Digits:=200: evalf((Catalan+sqrt(4+Catalan^2))/2, 1000):

%p numtheory[cfrac](%, 200,'quotients') ;

%t ContinuedFraction[(Catalan + Sqrt[4 + Catalan^2])/2, 84] (* _Michael De Vlieger_, Oct 23 2018 *)

%o (PARI) default(realprecision, 100); contfrac((Catalan+sqrt(4+Catalan^2))/2) \\ _Michel Marcus_, Oct 26 2018

%o (Magma) SetDefaultRealField(RealField(100)); R:=RealField();  ContinuedFraction((Catalan(R) + Sqrt(4 + Catalan(R)^2))/2); // _G. C. Greubel_, Oct 31 2018

%Y Cf. A006752, A188640, A320639 (decimal expansion).

%K nonn,cofr

%O 0,4

%A _Paolo P. Lava_, Oct 18 2018

%E Offset changed by _Andrew Howroyd_, Aug 10 2024