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 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. 1
 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 (list; constant; graph; refs; listen; history; text; internal format)
 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

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Last modified March 2 01:29 EST 2024. Contains 370447 sequences. (Running on oeis4.)