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
KEYWORD
nonn,cons
AUTHOR
Paolo P. Lava, Apr 11 2013
STATUS
approved