A320640 Continued fraction of (C + sqrt(4 + C^2))/2, where C is the Catalan constant.
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, 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, 1, 1, 3, 2, 1, 6, 2, 1, 1, 5, 16, 15, 2, 1, 4, 6, 120, 1, 1, 1
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..9999
Programs
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Magma
SetDefaultRealField(RealField(100)); R:=RealField(); ContinuedFraction((Catalan(R) + Sqrt(4 + Catalan(R)^2))/2); // G. C. Greubel, Oct 31 2018
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Maple
Digits:=200: evalf((Catalan+sqrt(4+Catalan^2))/2, 1000): numtheory[cfrac](%, 200,'quotients') ;
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Mathematica
ContinuedFraction[(Catalan + Sqrt[4 + Catalan^2])/2, 84] (* Michael De Vlieger, Oct 23 2018 *)
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PARI
default(realprecision, 100); contfrac((Catalan+sqrt(4+Catalan^2))/2) \\ Michel Marcus, Oct 26 2018
Extensions
Offset changed by Andrew Howroyd, Aug 10 2024
Comments