A245263 Decimal expansion of the minimum total length of lines tying together the five points of a regular pentagon having unit sides.

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

Offset

1,1

Links

Table of n, a(n) for n=1..101.

Jean-François Alcover, Pentagon Steiner tree. After James C. Bergquist.

Herman P. Robinson, Mathematical Constants. p. 182.

Index entries for algebraic numbers, degree 8

Formula

(7*sqrt(3)-sqrt(15))/12 + sqrt(18-6*sqrt(5))/3 + (1+sqrt(5))*sqrt(10-2*sqrt(5))/8 + sqrt(5+2*sqrt(5))/2 = sqrt(17+7*sqrt(5)+sqrt(6*(65+29*sqrt(5))))/2.

Example

3.891156823326853818078262556719905049852981445670139299627728956...

Mathematica

(7*Sqrt[3]-Sqrt[15])/12 + Sqrt[18-6*Sqrt[5]]/3 + (1+Sqrt[5])*Sqrt[10-2*Sqrt[5]]/8 + Sqrt[5+2*Sqrt[5]]/2 // RealDigits[#, 10, 101] & // First

Prog

(PARI) sqrt(polrootsreal(x^4-17*x^3+29*x^2-13*x+1)[4]) \\ Charles R Greathouse IV, Jul 15 2014
(PARI) polrootsreal(x^8-17*x^6+29*x^4-13*x^2+1)[8] \\ Charles R Greathouse IV, Oct 27 2023

Crossrefs

Sequence in context: A229372 A357406 A021261 * A016672 A177272 A010630

Adjacent sequences: A245260 A245261 A245262 * A245264 A245265 A245266

Keyword

nonn,cons

Author

Jean-François Alcover, Jul 15 2014

Status

approved