A224579 - OEIS

%I #19 Aug 09 2024 01:53:30

%S 1,3,28,13,3,1,2,1,1,8,3,4,3,3,15,12,5,2,8,1,24,2,3,5,1,1,3,3,1,1,1,2,

%T 1,1,7,12,1,1,1,3,1,1,1,2,1,107,1,3,6,1,26,121,3,2,1,1,12,117,1,2,3,7,

%U 5,41,5,1,5,1,1,2,3,1,200,1,4,3,191,1,5,3,5

%N Continued fraction of (gamma+sqrt(4+gamma^2))/2, where gamma is the Euler-Mascheroni constant.

%C Continued fraction of the constant in A224578.

%H Paolo P. Lava, <a href="/A224579/b224579.txt">Table of n, a(n) for n = 0..999</a>

%p Digits:=200; a:=evalf(gamma,5000); evalf((a+sqrt(4+a^2))/2,1000);

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

%t ContinuedFraction[(EulerGamma+Sqrt[4+EulerGamma^2])/2, 100] (* _G. C. Greubel_, Aug 30 2018 *)

%o (PARI) default(realprecision, 100); contfrac((Euler + sqrt(4 + Euler^2))/2) \\ _G. C. Greubel_, Aug 30 2018

%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); ContinuedFraction((EulerGamma(R) + Sqrt(4+EulerGamma(R)^2))/2); // _G. C. Greubel_, Aug 30 2018

%Y Cf. A001620, A188640, A224578 (decimal expansion).

%K nonn,cofr

%O 0,2

%A _Paolo P. Lava_, Apr 11 2013

%E Offset changed by _Andrew Howroyd_, Aug 08 2024