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A132116 Continued fraction expansion of Pi/sqrt(3) = sqrt(2*zeta(2)). 2
1, 1, 4, 2, 1, 2, 3, 7, 3, 3, 30, 2, 1, 2, 2, 83, 9, 20, 1, 37, 1, 2, 7, 1, 1, 2, 1, 6, 1, 2, 1, 1, 3, 3, 1, 4, 8, 1, 6, 33, 1, 1, 1, 17, 4, 1, 3, 1, 5, 3, 2, 1, 1100, 2, 31, 6, 7, 1, 1, 9, 6, 3, 1, 2, 2, 2, 1, 2, 4, 6, 16, 1, 1, 8, 1, 13, 2, 18, 1, 4, 1, 46, 2, 5, 1, 3, 1, 42, 1, 1, 1, 26, 3, 2, 1, 5, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Dolbeault et al. Abstract, where this is referred to as "the semiclassical constant" following remark 2, p. 2: "Following Eden and Foias we obtain a matrix version of a generalised Sobolev inequality in one-dimension. This allow us to improve on the known estimates of best constants in Lieb-Thirring inequalities for the sum of the negative eigenvalues for multi-dimensional Schroedinger operators."

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

Jean Dolbeault, Ari Laptev and Michael Loss, Lieb-Thirring inequalities with improved constants, arXiv:0708.1165 [math.AP], 2007.

EXAMPLE

1 + 1/1 + 1/4 + 1/2 + 1/1 + 1/2 + 1/3 + 1/7 + 1/3 + 1/3 + 1/30 + 1/2 + 1/1 + 1/2 + 1/2 + 1/83 + 1/9 + 1/20 + 1/1 + 1/37 + 1/1 + 1/2 + 1/7 + 1/1 + 1/1 + 1/2 + 1/1 + 1/6 + 1/1 + 1/2 + 1/1 + 1/1 + 1/3 + 1/3 + 1/1 + 1/4 + 1/8 + 1/1 + 1/6 + 1/33 + 1/1 + 1/1 + 1/1 + 1/17 + 1/4 + 1/1 + 1/3 + 1/1 + 1/5 + 1/3 + 1/2 + 1/1 + 1/1100 + 1/2 + 1/31 + 1/6 + 1/7 + 1/1 + 1/1 + 1/9 + 1/6 + 1/3 + 1/1 + 1/2 + 1/2 + 1/2 + 1/1 + 1/2 + 1/4 + 1/6 + 1/16 + 1/1 + 1/1 + 1/8 + 1/1 + 1/13 + 1/2 + 1/18 + 1/1 + 1/4 + 1/1 + 1/46 + 1/2 + 1/5 + 1/1 + 1/3 + 1/1 + 1/42 + 1/1 + 1/1 + 1/1 + 1/26 + 1/3 + 1/2 + 1/1 + 1/5 + 1/4 + 1/4 + 1/5 + 1/1 + . . .

MAPLE

with(numtheory): cfrac(Pi/(sqrt(3)), 100, 'quotients'); # Muniru A Asiru, Sep 28 2018

MATHEMATICA

ContinuedFraction[Pi/Sqrt[3], 100] (* G. C. Greubel, Sep 27 2018 *)

PROG

(PARI) default(realprecision, 100); contfrac(Pi/sqrt(3)) \\ G. C. Greubel, Sep 27 2018

(MAGMA) SetDefaultRealField(RealField(100)); R:= RealField(); ContinuedFraction(Pi(R)/Sqrt(3)); // G. C. Greubel, Sep 27 2018

CROSSREFS

Cf. A093602 (decimal expansion).

Sequence in context: A080816 A016507 A270047 * A229974 A281065 A280988

Adjacent sequences:  A132113 A132114 A132115 * A132117 A132118 A132119

KEYWORD

cofr,easy,nonn

AUTHOR

Jonathan Vos Post, Aug 10 2007

STATUS

approved

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Last modified May 22 05:03 EDT 2019. Contains 323473 sequences. (Running on oeis4.)