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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 (list; constant; graph; refs; listen; history; text; internal format)
 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

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Last modified December 10 04:38 EST 2023. Contains 367699 sequences. (Running on oeis4.)