A248411 Decimal expansion of the best lower bound for the Steiner ratio rho_3, the least upper bound on the ratio of the length of the Steiner minimal tree to the length of the minimal tree in dimension 3.

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.6 Steiner Tree Constants, p. 504.

Links

Table of n, a(n) for n=0..101.

Formula

b = (2 + x - sqrt(x^2 + x + 1))/sqrt(3), where x is the positive root of 128*x^6 + 456*x^5 + 783*x^4 + 764*x^3 + 408*x^2 + 108*x - 28.

Example

x = 0.1486637196311613967236467715222572732594626883945180141...
b = 0.6158277481234066067171143973014413934410965351332132943...

Mathematica

x0 = Root[128*x^6 + 456*x^5 + 783*x^4 + 764*x^3 + 408*x^2 + 108*x - 28, 2]; b = (2 + x0 - Sqrt[x0^2 + x0 + 1])/Sqrt[3]; RealDigits[b, 10, 102] // First

Crossrefs

Cf. A220351 (upper bound of rho_3).

Sequence in context: A019847 A021946 A257704 * A011439 A094774 A231925

Adjacent sequences: A248408 A248409 A248410 * A248412 A248413 A248414

Keyword

nonn,cons

Author

Jean-François Alcover, Oct 06 2014

Status

approved