

A233699


Ideal rectangle side length for packing squares with side 1/n.


1



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

0,1


COMMENTS

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).


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000
M. M. Paulhus, An Algorithm for Packing Squares, Journal of Combinatorial Theory,1998, A,82(2), pages 147157.
Pegg Jr, Ed., Wolfram Demonstrations Project, Packing Squares with Side 1/n
Wikipedia, Packing Squares with Side 1/n


FORMULA

Equals (Pi^26)/5 = A164102/10  6/5.


EXAMPLE

0.77392088021787172376689819997523022706273988144815812528266987524400896448...


MATHEMATICA

RealDigits[(Pi^26)/5, 10, 120][[1]] (* Harvey P. Dale, Aug 21 2017 *)


PROG

(PARI) (Pi^26)/5;
(MAGMA) C<i> := ComplexField(); (Pi(C)^26)/5 // G. C. Greubel, Jan 26 2018


CROSSREFS

Sequence in context: A212299 A193751 A290565 * A220052 A153204 A199508
Adjacent sequences: A233696 A233697 A233698 * A233700 A233701 A233702


KEYWORD

nonn,cons


AUTHOR

John W. Nicholson, Dec 15 2013


STATUS

approved



