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A214549 Decimal expansion of 4*Pi^2/27. 5
1, 4, 6, 2, 1, 6, 3, 6, 1, 4, 9, 7, 6, 2, 0, 1, 2, 7, 6, 8, 6, 4, 3, 6, 9, 0, 3, 7, 0, 1, 8, 6, 8, 9, 0, 5, 7, 0, 8, 3, 5, 1, 1, 0, 2, 3, 2, 9, 4, 9, 3, 1, 9, 4, 4, 6, 5, 3, 8, 2, 9, 5, 3, 7, 2, 1, 7, 7, 8, 4, 4, 1, 8, 1, 3, 6, 1, 7, 8, 5, 5, 4, 5, 1, 8, 7, 8, 1, 2, 4, 4, 9, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Represents the value of the Dirichlet series for A011655 (principal Dirichlet character mod 3) at s=2.

LINKS

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

R. J. Mathar, Table of Dirichlet L-Series, arXiv:1008.2547 [math.NT], 2010-2015, Table 22.

FORMULA

Equals (4/3)*A100044.

Equals Sum_{n>=0} (1/(3*n+1)^2 + 1/(3*n+2)^2).

From Peter Luschny, May 13 2020: (Start)

Equals (8/9) * Sum_(k>=1) 1/k^2.

Equals -(16/9) * Sum_(k>=1) (-1)^k/k^2.

Equals (64/27) * ( Integral_{x=0..1} sqrt(1 - x^2) )^2. (End)

Equals Integral_{x=0..oo} log(x)/(x^3 - 1) dx. - Amiram Eldar, Aug 12 2020

EXAMPLE

1.4621636149762012768643690370186...

MAPLE

evalf(4*Pi^2/27) ;

MATHEMATICA

RealDigits[(4Pi^2)/27, 10, 120][[1]] (* Harvey P. Dale, Dec 20 2012 *)

PROG

(PARI) 4*Pi^2/27 \\ G. C. Greubel, Mar 08 2018

(MAGMA) R:= RealField(); 4*Pi(R)^2/27; // G. C. Greubel, Mar 08 2018

(MAGMA) R:=RealField(106); SetDefaultRealField(R); n:=4*Pi(R)^2/27; Reverse(Intseq(Floor(10^105*n))); // Bruno Berselli, Mar 13 2018

(Julia)

using Nemo

R = RealField(310)

t = const_pi(RR) + const_pi(RR); s = t * t

s / RR(27) |> println # Peter Luschny, Mar 13 2018

CROSSREFS

Sequence in context: A016491 A160327 A124259 * A154892 A286155 A195860

Adjacent sequences:  A214546 A214547 A214548 * A214550 A214551 A214552

KEYWORD

nonn,cons,easy

AUTHOR

R. J. Mathar, Jul 20 2012

STATUS

approved

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Last modified September 26 11:48 EDT 2020. Contains 337371 sequences. (Running on oeis4.)