cp's OEIS Frontend

A246724 Decimal expansion of r_2, the second smallest radius for which a compact packing of the plane exists, with disks of radius 1 and r_2.

%I A246724 #41 Feb 10 2025 12:23:38
%S A246724 1,5,4,7,0,0,5,3,8,3,7,9,2,5,1,5,2,9,0,1,8,2,9,7,5,6,1,0,0,3,9,1,4,9,
%T A246724 1,1,2,9,5,2,0,3,5,0,2,5,4,0,2,5,3,7,5,2,0,3,7,2,0,4,6,5,2,9,6,7,9,5,
%U A246724 5,3,4,4,6,0,5,8,6,6,6,9,1,3,8,7,4,3,0,7,9,1,1,7,1,4,9,9,0,5,0,4,5,0,4
%N A246724 Decimal expansion of r_2, the second smallest radius for which a compact packing of the plane exists, with disks of radius 1 and r_2.
%C A246724 Essentially the same digit sequence as A176053 and A020832. - _R. J. Mathar_, Sep 06 2014
%C A246724 This equals the ratio of the radius of the inner Soddy circle and the common radius of the three kissing circles. See A343235, also for links. - _Wolfdieter Lang_, Apr 19 2021
%C A246724 Previous comment is, together with A176053, the answer to the 1st problem proposed during the 4th Canadian Mathematical Olympiad in 1972. - _Bernard Schott_, Mar 16 2022
%D A246724 Michael Doob, The Canadian Mathematical Olympiad & L'Olympiade Mathématique du Canada 1969-1993 - Canadian Mathematical Society & Société Mathématique du Canada, Problem 1, 1972, page 37, 1993.
%H A246724 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 A246724 The IMO Compendium, <a href="https://imomath.com/othercomp/Can/CanMO72.pdf">Problem 1</a>, 4th Canadian Mathematical Olympiad, 1972.
%H A246724 Samuel G. Moreno and Esther M. García, <a href="http://www.jstor.org/stable/10.4169/math.mag.86.1.015">New infinite products of cosines and Viète-like formulae</a>, Mathematics Magazine, Vol. 86, No. 1 (2013), pp. 15-25.
%H A246724 Bernard Schott, <a href="/A246724/a246724.png">Soddy circles</a>.
%H A246724 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>.
%H A246724 <a href="/index/O#Olympiads">Index to sequences related to Olympiads</a>.
%F A246724 Equals (2*sqrt(3) - 3)/3.
%F A246724 Equals A176053 - 2.
%F A246724 Equals -1 + sqrt(2) * sqrt(2-sqrt(2)) * sqrt(2-sqrt(2-sqrt(2))) * ... (Moreno and García, 2013). - _Amiram Eldar_, Jun 09 2022
%e A246724 0.154700538379251529018297561003914911295203502540253752...
%t A246724 RealDigits[(2*Sqrt[3] - 3)/3, 10, 103] // First
%o A246724 (PARI) 2/sqrt(3) - 1 \\ _Charles R Greathouse IV_, Feb 10 2025
%Y A246724 Cf. A246723 (r_1), A246725 (r_3), A246726 (r_4), A246727 (r_5), A002193 (r_6 = sqrt(2)-1), A246728 (r_7), A246729 (r_8), A246730 (r_9).
%Y A246724 Cf. A176053, A343235.
%K A246724 nonn,cons,easy
%O A246724 0,2
%A A246724 _Jean-François Alcover_, Sep 02 2014