|
%I #37 Aug 10 2023 05:50:29
%S 2,1,5,4,7,0,0,5,3,8,3,7,9,2,5,1,5,2,9,0,1,8,2,9,7,5,6,1,0,0,3,9,1,4,
%T 9,1,1,2,9,5,2,0,3,5,0,2,5,4,0,2,5,3,7,5,2,0,3,7,2,0,4,6,5,2,9,6,7,9,
%U 5,5,3,4,4,6,0,5,8,6,6,6,9,1,3,8,7,4,3,0,7,9,1,1,7,1,4,9,9,0,5,0,4,5,0,4,1
%N Decimal expansion of (3+2*sqrt(3))/3.
%C Continued fraction expansion of (3+2*sqrt(3))/3 is A010696.
%C a(n) = A020832(n-1) for n > 1; a(1) = 2.
%C This equals the ratio of the radius of the outer Soddy circle and the common radius of the three kissing circles. See A343235, also for links. - _Wolfdieter Lang_, Apr 19 2021
%C Previous comment is, together with A246724, the answer to the 1st problem proposed during the 4th Canadian Mathematical Olympiad in 1972. - _Bernard Schott_, Mar 20 2022
%D 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 Paolo Xausa, <a href="/A176053/b176053.txt">Table of n, a(n) for n = 1..10000</a>
%H The IMO Compendium, <a href="https://imomath.com/othercomp/Can/CanMO72.pdf">Problem 1</a>, 4th Canadian Mathematical Olympiad, 1972.
%H Michael Penn, <a href="https://www.youtube.com/watch?v=57vj5lIjSto">An inscribed tower of squares</a>, YouTube video, 2020.
%H Bernard Schott, <a href="/A246724/a246724.png">Illustration of the Soddy circles</a>.
%H <a href="/index/O#Olympiads">Index to sequences related to Olympiads</a>.
%F Equals 2 + A246724.
%e 2.15470053837925152901...
%t RealDigits[1+2/3Sqrt[3],10,100][[1]] (* _Paolo Xausa_, Aug 10 2023 *)
%Y Cf. A002194 (sqrt(3)), A020832 (1/sqrt(75)), A010696 (repeat 2, 6).
%Y Cf. A246724, A343235.
%K nonn,cons
%O 1,1
%A _Klaus Brockhaus_, Apr 07 2010
|
