A224578 Decimal expansion of (gamma+sqrt(4+gamma^2))/2, where gamma is the Euler-Mascheroni constant.

1, 3, 2, 9, 4, 2, 2, 1, 6, 7, 9, 3, 6, 1, 7, 3, 5, 8, 1, 8, 7, 9, 4, 1, 7, 7, 6, 8, 1, 0, 5, 6, 3, 6, 2, 4, 4, 8, 0, 8, 4, 9, 5, 8, 3, 3, 2, 9, 2, 0, 0, 0, 8, 3, 0, 4, 4, 2, 6, 2, 1, 4, 6, 5, 7, 4, 2, 5, 8, 1, 9, 9, 6, 9, 1, 3, 2, 6, 1, 7, 8, 1, 2, 2, 7, 6, 7

Offset

1,2

Comments

Decimal expansion of shape of a gamma-extension rectangle; see A188640 for definitions of shape and r-extension rectangle.

Specifically, for a gamma-extension rectangle, 1 square is removed first, then 3 squares, then 28 squares, then 13 squares, then 3 squares,...(see A224579), so that the original rectangle is partitioned into an infinite collection of squares.

Links

Paolo P. Lava, Table of n, a(n) for n = 1..200

Clark Kimberling, Two kinds of golden triangles, generalized to match continued fractions, Journal for Geometry and Graphics, 11 (2007) 165-171

Example

1.329422167936173581879417768105... = [gamma, gamma, gamma, ...]

Maple

evalf((gamma+sqrt(4+gamma^2))/2, 90);

Mathematica

RealDigits[(EulerGamma + Sqrt[4 + EulerGamma^2])/2, 10, 100][[1]] (* G. C. Greubel, Aug 30 2018 *)

Prog

(PARI) Euler/2+sqrt(4+Euler^2)/2 \\ Charles R Greathouse IV, Dec 11 2013
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (EulerGamma(R) + Sqrt(4 + EulerGamma(R)^2))/2; // G. C. Greubel, Aug 30 2018

Crossrefs

Cf. A001620, A188640, A224579.

Sequence in context: A192492 A351444 A104005 * A134562 A090639 A294370

Adjacent sequences: A224575 A224576 A224577 * A224579 A224580 A224581

Keyword

nonn,cons

Author

Paolo P. Lava, Apr 11 2013

Status

approved