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A320640
Continued fraction of (C + sqrt(4 + C^2))/2, where C is the Catalan constant.
2
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
0,4
COMMENTS
Continued fraction of the constant in A320639.
LINKS
MAPLE
Digits:=200: evalf((Catalan+sqrt(4+Catalan^2))/2, 1000):
numtheory[cfrac](%, 200, 'quotients') ;
MATHEMATICA
ContinuedFraction[(Catalan + Sqrt[4 + Catalan^2])/2, 84] (* Michael De Vlieger, Oct 23 2018 *)
PROG
(PARI) default(realprecision, 100); contfrac((Catalan+sqrt(4+Catalan^2))/2) \\ Michel Marcus, Oct 26 2018
(Magma) SetDefaultRealField(RealField(100)); R:=RealField(); ContinuedFraction((Catalan(R) + Sqrt(4 + Catalan(R)^2))/2); // G. C. Greubel, Oct 31 2018
CROSSREFS
Cf. A006752, A188640, A320639 (decimal expansion).
Sequence in context: A144211 A260510 A125291 * A055187 A217780 A329316
KEYWORD
nonn,cofr
AUTHOR
Paolo P. Lava, Oct 18 2018
EXTENSIONS
Offset changed by Andrew Howroyd, Aug 10 2024
STATUS
approved