A246727 - OEIS

%I #19 Mar 27 2022 03:50:33

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

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

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

%N Decimal expansion of r_5, the 5th smallest radius < 1 for which a compact packing of the plane exists, with disks of radius 1 and r_5.

%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 1st root of 9x^4 - 12x^3 - 26x^2 - 12x + 9.

%F Equals (1 + 2*sqrt(3) - 2*sqrt(1 + sqrt(3)))/3. - _Amiram Eldar_, Mar 27 2022

%e 0.3861061048585385422861371299469896994436146884586173...

%t RealDigits[Root[9x^4 - 12x^3 - 26x^2 - 12x + 9, x, 1], 10, 104] // First

%Y Cf. A246723 (r_1), A246724 (r_2), A246725 (r_3), A246726 (r_4), A002193 (r_6 = sqrt(2)-1), A246728 (r_7), A246729 (r_8), A246730 (r_9).

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, Sep 02 2014