A176053 Decimal expansion of (3+2*sqrt(3))/3.

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, 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, 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

Offset: 1

Author

Klaus Brockhaus, Apr 07 2010

Keywords

• nonn
• cons

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

Examples

			2.15470053837925152901...
		

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.
• Index to sequences related to Olympiads.

Crossrefs

Cf. A002194 (sqrt(3)), A020832 (1/sqrt(75)), A010696 (repeat 2, 6).

Cf. A246724, A343235.

Programs

Mathematica

RealDigits[1+2/3Sqrt[3],10,100][[1]] (* Paolo Xausa, Aug 10 2023 *)

Formula

Equals 2 + A246724.