cp's OEIS Frontend

A246727 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.

%I A246727 #21 Feb 10 2025 12:22:28
%S A246727 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 A246727 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 A246727 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 A246727 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 A246727 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.
%H A246727 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.
%F A246727 1st root of 9x^4 - 12x^3 - 26x^2 - 12x + 9.
%F A246727 Equals (1 + 2*sqrt(3) - 2*sqrt(1 + sqrt(3)))/3. - _Amiram Eldar_, Mar 27 2022
%e A246727 0.3861061048585385422861371299469896994436146884586173...
%t A246727 RealDigits[Root[9x^4 - 12x^3 - 26x^2 - 12x + 9, x, 1], 10, 104] // First
%o A246727 (PARI) (1 + 2*sqrt(3) - 2*sqrt(1 + sqrt(3)))/3 \\ _Charles R Greathouse IV_, Feb 10 2025
%Y A246727 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 A246727 nonn,cons,easy
%O A246727 0,1
%A A246727 _Jean-François Alcover_, Sep 02 2014