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A233699
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Ideal rectangle side length for packing squares with side 1/n.
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1
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7, 7, 3, 9, 2, 0, 8, 8, 0, 2, 1, 7, 8, 7, 1, 7, 2, 3, 7, 6, 6, 8, 9, 8, 1, 9, 9, 9, 7, 5, 2, 3, 0, 2, 2, 7, 0, 6, 2, 7, 3, 9, 8, 8, 1, 4, 4, 8, 1, 5, 8, 1, 2, 5, 2, 8, 2, 6, 6, 9, 8, 7, 5, 2, 4, 4, 0, 0, 8, 9, 6, 4, 4, 8, 3, 8, 4, 1, 0, 4, 8, 6
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OFFSET
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0,1
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COMMENTS
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With one side s_1 = 1/2+1/3 = 5/6, and with area A = s_1*s_2 = sum(n=2,infinity, 1/n^2) = Pi^2/6 - 1 = A013661 - 1, the second side, s_2, can be solved.
The current packing record holder is Marc Paulhus, who developed a packing algorithm (see Link).
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LINKS
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FORMULA
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Equals (Pi^2-6)/5 = A164102/10 - 6/5.
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EXAMPLE
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0.77392088021787172376689819997523022706273988144815812528266987524400896448...
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MATHEMATICA
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RealDigits[(Pi^2-6)/5, 10, 120][[1]] (* Harvey P. Dale, Aug 21 2017 *)
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PROG
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(PARI) (Pi^2-6)/5;
(Magma) C<i> := ComplexField(); (Pi(C)^2-6)/5 // G. C. Greubel, Jan 26 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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