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A320639
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Decimal expansion of (C + sqrt(4 + C^2))/2, where C is the Catalan constant.
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2
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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1.557868355876025567309823249177... = [Catalan, Catalan, Catalan, ...]
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MAPLE
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evalf((Catalan+sqrt(4+Catalan^2))/2, 135);
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MATHEMATICA
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First@ RealDigits[(Catalan + Sqrt[4 + Catalan^2])/2, 10, 105] (* Michael De Vlieger, Oct 23 2018 *)
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PROG
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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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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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