A224579 Continued fraction of (gamma+sqrt(4+gamma^2))/2, where gamma is the Euler-Mascheroni constant.

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

Offset

0,2

Comments

Continued fraction of the constant in A224578.

Links

Paolo P. Lava, Table of n, a(n) for n = 0..999

Maple

Digits:=200; a:=evalf(gamma, 5000); evalf((a+sqrt(4+a^2))/2, 1000);
numtheory[cfrac](%, 200, 'quotients') ;

Mathematica

ContinuedFraction[(EulerGamma+Sqrt[4+EulerGamma^2])/2, 100] (* G. C. Greubel, Aug 30 2018 *)

Prog

(PARI) default(realprecision, 100); contfrac((Euler + sqrt(4 + Euler^2))/2) \\ G. C. Greubel, Aug 30 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); ContinuedFraction((EulerGamma(R) + Sqrt(4+EulerGamma(R)^2))/2); // G. C. Greubel, Aug 30 2018

Crossrefs

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

Sequence in context: A188927 A146072 A064234 * A037102 A042169 A041785

Adjacent sequences: A224576 A224577 A224578 * A224580 A224581 A224582

Keyword

nonn,cofr

Author

Paolo P. Lava, Apr 11 2013

Extensions

Offset changed by Andrew Howroyd, Aug 08 2024

Status

approved