A277390 Decimal expansion of 5-2*sqrt(5)+sqrt(25-10*sqrt(5))-sqrt(5-2*sqrt(5)).

1, 4, 2, 5, 9, 1, 9, 9, 9, 8, 1, 5, 9, 5, 9, 1, 3, 5, 2, 0, 6, 5, 5, 4, 2, 9, 6, 6, 1, 3, 2, 5, 0, 1, 1, 0, 4, 2, 7, 7, 1, 8, 8, 2, 4, 5, 4, 1, 9, 1, 1, 5, 5, 9, 0, 2, 4, 7, 1, 6, 2, 7, 7, 7, 5, 1, 6, 5, 7, 3, 2, 6, 1, 6, 8, 2, 4, 3, 1, 8, 5, 4, 3, 6, 4, 0, 3

Offset

1,2

Comments

Largest radius of five circles tangent to a circle of radius 1.

A quartic integer with minimal polynomial x^4 - 20x^3 + 10x^2 + 20x + 5. - Charles R Greathouse IV, Oct 12 2016

Links

Table of n, a(n) for n=1..87.

Eric W. Weisstein: Steiner chain. From MathWorld. A Wolfram Web Resource.

Index entries for algebraic numbers, degree 4

Formula

tan(Pi/5)*(tan(Pi/5)+sqrt(1+tan(Pi/5)^2)).

Example

1.42591999815959135206...

Mathematica

RealDigits[5-2*Sqrt[5]+Sqrt[25-10*Sqrt[5]]-Sqrt[5-2*Sqrt[5]], 10, 120][[1]] (* Harvey P. Dale, May 20 2021 *)

Prog

(PARI) s=sqrt(5); t=5-2*s; sqrt(25-10*s)+t-sqrt(t) \\ Charles R Greathouse IV, Oct 12 2016

Crossrefs

Cf. A176394 (three circles), A014176 (four circles).

Sequence in context: A112962 A226457 A349244 * A200608 A163358 A121709

Adjacent sequences: A277387 A277388 A277389 * A277391 A277392 A277393

Keyword

nonn,cons

Author

Martin Renner, Oct 12 2016

Status

approved