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A093954
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Decimal expansion of Pi/(2*sqrt(2)).
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5
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1, 1, 1, 0, 7, 2, 0, 7, 3, 4, 5, 3, 9, 5, 9, 1, 5, 6, 1, 7, 5, 3, 9, 7, 0, 2, 4, 7, 5, 1, 5, 1, 7, 3, 4, 2, 4, 6, 5, 3, 6, 5, 5, 4, 2, 2, 3, 4, 3, 9, 2, 2, 5, 5, 5, 7, 7, 1, 3, 4, 8, 9, 0, 1, 7, 3, 9, 1, 0, 8, 6, 9, 8, 2, 7, 4, 8, 6, 8, 4, 7, 7, 6, 4, 3, 8, 3, 1, 7, 3, 3, 6, 9, 1, 1, 9, 1, 3, 0, 9, 3, 4
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Contribution from Eric Desbiaux (moongerms(AT)wanadoo.fr), Jan 18 2009: (Start)
The value is the length Pi*sqrt(2)/4 of the diagonal in the square with side length Pi/4 = sum_{n>=0} (-1)^n/(2n+1) = A003881. The area of the circumcircle of this square is Pi*(Pi*sqrt(2)/8)^2 =Pi^3/32 =A153071.
(End)
This is the value of the Dirichlet L-function of modulus m=8 at argument s=1 for the non-principal character (1,0,1,0,-1,0,-1,0). See arXiv:1008.2547. - R. J. Mathar, Mar 22 2011
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REFERENCES
| Jolley, Summation of Series, Dover (1961) eq 76 page 16.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,20000
R. J. Mathar, Table of Dirichlet L-series and prime zeta modulo functions for small moduli, arXiv:1008.2547, table 7 and section 2.2, value of L(m=8,r=4,s=1).
Eric Weisstein's World of Mathematics, Bifoliate
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EXAMPLE
| 1.11072073... = 1/A112628.
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PROG
| (PARI) { default(realprecision, 20080); x=Pi*sqrt(2)/4; for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b093954.txt", n, " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 17 2009]
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CROSSREFS
| Cf. A161684 Continued fraction. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 17 2009]
Sequence in context: A056009 A159252 A102771 * A177703 A200338 A153589
Adjacent sequences: A093951 A093952 A093953 * A093955 A093956 A093957
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KEYWORD
| nonn,cons,easy
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com), Apr 19, 2004
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