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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 (list; constant; graph; refs; listen; history; text; internal format)
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

G. C. Greubel, Table of n, a(n) for n = 0..10000

Michel Waldschmidt, Perfect Powers: Pillai's works and their developments, Aug 27, 2009.

FORMULA

Equals Sum_{n>=0} Sum_{m>=0} 1/((4*n+3)^(2*m+1)).

Equals Sum_{k>=1} 1/( (4k-2)*(4k-1)*(4k)) ). - 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. A001597, A019675, A016655.

Cf. A195909, A195913, A195697. - Mohammad K. Azarian, Oct 11 2011

Cf. A239362: Sum_{k>=1} 1/((3k-2)*(3k-1)*(3k)) ).

Sequence in context: A238582 A154748 A190282 * A248938 A106144 A154478

Adjacent sequences:  A164830 A164831 A164832 * A164834 A164835 A164836

KEYWORD

nonn,cons

AUTHOR

Jonathan Vos Post, Aug 27 2009

EXTENSIONS

Normalized offset and leading zeros - R. J. Mathar, Sep 27 2009

STATUS

approved

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Last modified December 5 04:10 EST 2021. Contains 349530 sequences. (Running on oeis4.)