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

Author

Paolo P. Lava, Apr 11 2013

Keywords

• nonn
• cons

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.

Examples

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

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

Crossrefs

Cf. A001620, A188640, A224579.

Programs

Magma

SetDefaultRealField(RealField(100)); R:= RealField(); (EulerGamma(R) + Sqrt(4 + EulerGamma(R)^2))/2; // G. C. Greubel, Aug 30 2018

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 *)

PARI

Euler/2+sqrt(4+Euler^2)/2 \\ Charles R Greathouse IV, Dec 11 2013