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A086722 Decimal expansion of g(1)+g(2)-g(4)-g(5), where g(k) = sum(1/(6*m+k)^2,m=0..infinity). 10
1, 1, 7, 1, 9, 5, 3, 6, 1, 9, 3, 4, 4, 7, 2, 9, 4, 4, 5, 3, 0, 0, 7, 8, 1, 1, 4, 4, 4, 3, 6, 1, 3, 8, 5, 3, 4, 5, 4, 7, 7, 0, 1, 5, 0, 4, 8, 1, 7, 9, 2, 8, 1, 3, 0, 3, 3, 3, 1, 5, 0, 0, 9, 4, 4, 5, 0, 3, 3, 0, 4, 7, 6, 9, 7, 7, 4, 2, 7, 3, 2, 7, 1, 3, 9, 3, 0, 4, 3, 5, 6, 2, 4, 8, 3, 1, 4, 7, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

By summing over g(1)-g(5) and g(2)-g(4) separately we obtain A214552 for the first difference and a quarter of A086724 for the second difference. - R. J. Mathar, Jul 20 2012

2/3 times this constant equals A086724 [Bailey, Borwein and Crandall, J. Phys. A 39 (2006) 12271] - R. J. Mathar, Jul 20 2012

REFERENCES

L. Fejes Toth, Lagerungen in der Ebene, auf der Kugel und im Raum, 2nd. ed., Springer-Verlag, Berlin, Heidelberg 1972; see p. 213.

LINKS

Table of n, a(n) for n=1..99.

FORMULA

Equals -integral_{0..1} log(x)/(x^2-x+1) dx. - Jean-François Alcover, Aug 29 2014

EXAMPLE

1.1719536193447294453... = A214552 + A086724/4 = 1/1^2 +1/2^2 -1/4^2 -1/5^2 +1/7^2 +1/8^2 -1/10^2 -1/11^2 ++--....

MATHEMATICA

g[k_] := PolyGamma[1, k/6]/36; RealDigits[g[1] + g[2] - g[4] - g[5], 10, 99] // First (* Jean-François Alcover, Feb 12 2013 *)

CROSSREFS

Cf. A086723-A086731.

Sequence in context: A153870 A176437 A199463 * A296848 A282823 A200500

Adjacent sequences:  A086719 A086720 A086721 * A086723 A086724 A086725

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane, Jul 31 2003

STATUS

approved

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Last modified October 14 07:31 EDT 2019. Contains 327995 sequences. (Running on oeis4.)