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A196522 Decimal expansion of Pi*(1+sqrt(2))/8. 1
9, 4, 8, 0, 5, 9, 4, 4, 8, 9, 6, 8, 5, 1, 9, 9, 3, 5, 6, 8, 4, 8, 1, 5, 5, 4, 6, 6, 6, 7, 5, 2, 4, 5, 7, 2, 8, 5, 1, 4, 7, 3, 8, 8, 6, 0, 9, 3, 8, 4, 9, 5, 0, 5, 5, 0, 7, 5, 4, 2, 5, 2, 4, 9, 0, 8, 0, 3, 1, 3, 9, 9, 9, 2, 3, 2, 1, 0, 3, 6, 3, 6, 5, 0, 4, 2, 0, 2, 2, 0, 0, 1, 3, 3, 6, 0, 2, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
This is the mean of two Dirichlet L=functions modulo m=8 at s=1, one with character (1,0,-1,0,1,0,-1,0) as in A101455, the other with character (1,0,1,0,-1,0,-1,0).
The area of a circle circumscribed in a unit-area regular octagon. - Amiram Eldar, Nov 05 2020
REFERENCES
L. B. W. Jolley, Summation of series, Dover (1961), eq. 78 page 16 and eq. 264 page 48.
LINKS
FORMULA
Equals (1 - 1/7) + (1/9 - 1/15) + ... + (1/(1+8*k) - 1/(7+8*k)) + ... = (A093954 + A003881)/2.
EXAMPLE
0.948059448968519935684815...
MATHEMATICA
RealDigits[Pi*(1+Sqrt[2])/8, 10, 120][[1]] (* Harvey P. Dale, May 31 2013 *)
PROG
(PARI) default(realprecision, 100); Pi*(1+sqrt(2))/8 \\ G. C. Greubel, Oct 05 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)*(1+Sqrt(2))/8; // G. C. Greubel, Oct 05 2018
CROSSREFS
Sequence in context: A199665 A113273 A011460 * A334114 A268315 A019659
KEYWORD
nonn,cons,easy
AUTHOR
R. J. Mathar, Oct 03 2011
STATUS
approved

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Last modified March 29 04:59 EDT 2024. Contains 371264 sequences. (Running on oeis4.)