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A224578
Decimal expansion of (gamma+sqrt(4+gamma^2))/2, where gamma is the Euler-Mascheroni constant.
2
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
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
KEYWORD
nonn,cons
AUTHOR
Paolo P. Lava, Apr 11 2013
STATUS
approved