OFFSET
1,1
COMMENTS
Continued fraction expansion of (3+2*sqrt(3))/3 is A010696.
a(n) = A020832(n-1) for n > 1; a(1) = 2.
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
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
REFERENCES
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.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..10000
The IMO Compendium, Problem 1, 4th Canadian Mathematical Olympiad, 1972.
Michael Penn, An inscribed tower of squares, YouTube video, 2020.
Bernard Schott, Illustration of the Soddy circles.
FORMULA
Equals 2 + A246724.
EXAMPLE
2.15470053837925152901...
MATHEMATICA
RealDigits[1+2/3Sqrt[3], 10, 100][[1]] (* Paolo Xausa, Aug 10 2023 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Klaus Brockhaus, Apr 07 2010
STATUS
approved