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Decimal expansion of r_8, the 8th smallest radius < 1 for which a compact packing of the plane exists, with disks of radius 1 and r_8.
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%I #15 Jan 17 2020 16:02:33

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

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

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

%N Decimal expansion of r_8, the 8th smallest radius < 1 for which a compact packing of the plane exists, with disks of radius 1 and r_8.

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 62.

%F 3rd root of x^8 - 8x^7 - 44x^6 - 232x^5 - 482x^4 - 24x^3 + 388x^2 - 120x + 9.

%e 0.5451510421225726875938077183373486963843555749734647529253568...

%t RealDigits[Root[x^8 - 8x^7 - 44x^6 - 232x^5 - 482x^4 - 24x^3 + 388x^2 - 120x + 9, x, 3], 10, 101] // First

%Y Cf. A246723 (r_1), A246724 (r_2), A246725 (r_3), A246726 (r_4), A246727 (r_5), A002193 (r_6 = sqrt(2)-1), A246728 (r_7), A246730 (r_9).

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, Sep 02 2014