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

1,1

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.

Index to sequences related to Olympiads.

Formula

Equals 2 + A246724.

Example

2.15470053837925152901...

Mathematica

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

Crossrefs

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

Cf. A246724, A343235.

Sequence in context: A262219 A249905 A171175 * A259791 A325771 A207480

Adjacent sequences: A176050 A176051 A176052 * A176054 A176055 A176056

Keyword

nonn,cons

Author

Klaus Brockhaus, Apr 07 2010

Status

approved