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A320639 Decimal expansion of (C + sqrt(4 + C^2))/2, where C is the Catalan constant. 2
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Decimal expansion of the shape of a Catalan-extension rectangle; see A188640 for definitions of shape and r-extension rectangle.
Specifically, for a Catalan-extension rectangle, 1 square is removed first, then 1 square, then 1 square again, then 3 squares, then 1 square, ... (see A320640), 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
1.557868355876025567309823249177... = [Catalan, Catalan, Catalan, ...]
MAPLE
evalf((Catalan+sqrt(4+Catalan^2))/2, 135);
MATHEMATICA
First@ RealDigits[(Catalan + Sqrt[4 + Catalan^2])/2, 10, 105] (* Michael De Vlieger, Oct 23 2018 *)
PROG
(PARI) (Catalan+sqrt(4+Catalan^2))/2 \\ Felix Fröhlich, Oct 23 2018
(Magma) R:= RealField(200); (Catalan(R) + Sqrt(4 + Catalan(R)^2)) / 2; // Vincenzo Librandi, Oct 24 2018
CROSSREFS
Sequence in context: A028278 A095943 A120220 * A153105 A201523 A196348
KEYWORD
nonn,cons
AUTHOR
Paolo P. Lava, Oct 18 2018
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)