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Decimal expansion of r_4, the 4th smallest radius < 1 for which a compact packing of the plane exists, with disks of radius 1 and r_4.
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%I #20 Mar 27 2022 03:51:03

%S 3,4,9,1,9,8,1,8,6,2,0,8,5,4,9,8,7,6,4,7,3,6,2,3,2,3,7,0,4,5,6,9,4,3,

%T 1,5,2,7,8,2,6,2,0,4,9,8,4,3,7,4,7,5,0,7,1,9,1,4,5,1,0,9,3,9,9,1,4,8,

%U 6,6,7,2,4,2,6,2,0,9,7,3,7,0,4,3,0,5,5,8,8,0,6,4,6,7,1,8,5,3,8,0,7,8,2

%N Decimal expansion of r_4, the 4th smallest radius < 1 for which a compact packing of the plane exists, with disks of radius 1 and r_4.

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, arXiv:2001.00578 [math.HO], 2020-2021, p. 73.

%F 3rd root of x^4 - 28x^3 - 10x^2 + 4x + 1.

%F Equals 1/(cosec(Pi/12)-1) = 1/(A214726 - 1). - _Amiram Eldar_, Mar 27 2022

%e 0.3491981862085498764736232370456943152782620498437475...

%t RealDigits[Root[x^4 - 28x^3 - 10x^2 + 4x + 1, x, 3], 10, 103] // First

%Y Cf. A246723 (r_1), A246724 (r_2), A246725 (r_3), A246727 (r_5), A002193 (r_6 = sqrt(2)-1), A246728 (r_7), A246729 (r_8), A246730 (r_9).

%Y Cf. A214726.

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, Sep 02 2014