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A164833
Decimal expansion of Pi/8 - log(2)/2.
5
0, 4, 6, 1, 2, 5, 4, 9, 1, 4, 1, 8, 7, 5, 1, 5, 0, 0, 0, 9, 9, 2, 1, 4, 3, 6, 2, 1, 8, 0, 8, 4, 9, 5, 7, 6, 4, 8, 6, 8, 9, 6, 1, 0, 7, 7, 4, 1, 7, 6, 0, 6, 0, 0, 5, 6, 1, 5, 2, 8, 0, 6, 9, 2, 9, 1, 7, 8, 0, 2, 3, 9, 8, 0, 0, 9, 2, 8, 7, 6, 7, 0, 2, 5, 5, 7, 2, 6, 8, 9, 6, 6, 9, 5, 5, 5, 2, 8, 9, 7, 2, 6, 7, 6, 7, 7, 7, 0, 3, 0, 3, 8, 7, 4, 9, 4, 5, 4, 6
OFFSET
0,2
COMMENTS
Digits and formula given at Waldschmidt, p. 4.
REFERENCES
Mohammad K. Azarian, Problem 1218, Pi Mu Epsilon Journal, Vol. 13, No. 2, Spring 2010, p. 116. Solution published in Vol. 13, No. 3, Fall 2010, pp. 183-185.
L. B. W. Jolley, Summation of series, Dover Publications Inc. (New York), 1961, p. 46 (series n. 251).
A. J. Van Der Poorten, Effectively computable bounds for the solutions of certain Diophantine equations, Acta Arith., 33 (1977), pp. 195-207.
LINKS
FORMULA
Equals Sum_{n>=0} Sum_{m>=0} 1/((4*n+3)^(2*m+1)).
Equals Sum_{k>=1} 1/( (4*k-2)*(4*k-1)*(4*k) ). - Bruno Berselli, Mar 17 2014
EXAMPLE
0.0461254914187515000992143621808495764868961077417606...
1/(2*3*4) + 1/(6*7*8) + 1/(10*11*12) + 1/(14*15*16) + ... [Bruno Berselli, Mar 17 2014]
MAPLE
evalf[130]((Pi - 4*log(2))/8 ); # G. C. Greubel, Aug 11 2019
MATHEMATICA
Join[{0}, RealDigits[Pi/8-Log[2]/2, 10, 120][[1]]] (* Harvey P. Dale, Nov 13 2012 *)
PROG
(PARI) default(realprecision, 130); (Pi - 4*log(2))/8 \\ G. C. Greubel, Aug 11 2019
(Magma) SetDefaultRealField(RealField(130)); R:= RealField(); (Pi(R)-4*Log(2))/8; // G. C. Greubel, Aug 11 2019
(Sage) numerical_approx((pi-4*log(2))/8, digits=130) # G. C. Greubel, Aug 11 2019
CROSSREFS
Cf. A239362: Sum_{k>=1} 1/((3k-2)*(3k-1)*(3k)).
Sequence in context: A238582 A154748 A190282 * A248938 A106144 A154478
KEYWORD
nonn,cons,easy
AUTHOR
Jonathan Vos Post, Aug 27 2009
EXTENSIONS
Normalized offset and leading zeros - R. J. Mathar, Sep 27 2009
STATUS
approved