A320639 Decimal expansion of (C + sqrt(4 + C^2))/2, where C is the Catalan constant.
1, 5, 5, 7, 8, 6, 8, 3, 5, 5, 8, 7, 6, 0, 2, 5, 5, 6, 7, 3, 0, 9, 8, 2, 3, 2, 4, 9, 1, 7, 7, 4, 0, 6, 9, 9, 0, 6, 9, 7, 1, 6, 4, 3, 1, 0, 8, 6, 0, 1, 3, 3, 6, 0, 2, 3, 2, 1, 4, 7, 9, 8, 0, 1, 4, 0, 5, 9, 5, 6, 7, 1, 1, 2, 7, 4, 4, 7, 4, 0, 4, 8, 3, 1, 9, 9, 0, 7, 7, 2, 5, 6, 6, 2, 0, 9, 2, 9, 4, 1, 5, 5, 9, 4, 5, 5, 2, 9, 9, 1, 3, 3, 3, 3, 9, 2, 3, 4, 3, 3, 7, 0, 4, 6, 6, 9, 5, 9, 0, 9, 4
Offset: 1
Examples
1.557868355876025567309823249177... = [Catalan, Catalan, Catalan, ...]
Links
- G. C. Greubel, Table of n, a(n) for n = 1..10000
- Clark Kimberling, Two kinds of golden triangles, generalized to match continued fractions, Journal for Geometry and Graphics, 11 (2007) 165-171.
Programs
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Magma
R:= RealField(200); (Catalan(R) + Sqrt(4 + Catalan(R)^2)) / 2; // Vincenzo Librandi, Oct 24 2018
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Maple
evalf((Catalan+sqrt(4+Catalan^2))/2,135);
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Mathematica
First@ RealDigits[(Catalan + Sqrt[4 + Catalan^2])/2, 10, 105] (* Michael De Vlieger, Oct 23 2018 *)
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PARI
(Catalan+sqrt(4+Catalan^2))/2 \\ Felix Fröhlich, Oct 23 2018
Comments