cp's OEIS Frontend

A246723 Decimal expansion of r_1, the smallest radius for which a compact packing of the plane exists, with disks of radius 1 and r_1.

%I A246723 #27 Aug 21 2023 12:21:54
%S A246723 1,0,1,0,2,0,5,1,4,4,3,3,6,4,3,8,0,3,6,0,5,4,3,1,8,5,0,5,8,8,2,1,7,2,
%T A246723 1,6,0,6,8,1,0,5,0,3,8,6,8,6,6,5,9,7,4,3,1,3,4,6,1,4,8,6,5,4,9,8,0,7,
%U A246723 9,2,4,5,0,8,5,3,6,9,9,4,6,9,2,0,2,8,1,1,3,3,7,9,0,7,1,9,5,3,0,3,6,2,8,1
%N A246723 Decimal expansion of r_1, the smallest radius for which a compact packing of the plane exists, with disks of radius 1 and r_1.
%H A246723 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. 62.
%H A246723 Gabriel Klambauer, <a href="https://doi.org/10.2307/2321992">Summation of Series</a>, Amer. Math. Monthly, Vol. 87, No. 2 (Feb., 1980), pp. 128-130.
%H A246723 Wikipedia, <a href="https://en.wikipedia.org/wiki/Engel_expansion">Engel expansion</a>
%H A246723 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F A246723 Equals 5 - 2*sqrt(6).
%F A246723 Equals Sum_{k>=1} binomial(2*k,k)/((k+1) * 12^k). - _Amiram Eldar_, Oct 04 2021
%F A246723 Engel expansion of 5 - 2*sqrt(6) = 1/10 + 1/(10*98) + 1/(10*98*9602) + ..., where [10, 98, 9602, ...] = A135927. See Klambauer, p. 130. - _Peter Bala_, Feb 01 2022
%F A246723 Equals exp(-arccosh(5)). - _Amiram Eldar_, Jul 06 2023
%e A246723 0.101020514433643803605431850588217216068105038686659743...
%t A246723 RealDigits[5 - 2*Sqrt[6], 10, 104] // First
%Y A246723 Cf. A246724 (r_2), A246725 (r_3), A246726 (r_4), A246727 (r_5), A002193 (r_6 = sqrt(2)-1), A246728 (r_7), A246729 (r_8), A246730 (r_9).
%K A246723 nonn,cons,easy
%O A246723 0,5
%A A246723 _Jean-François Alcover_, Sep 02 2014