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A295874 Decimal expansion of the real positive fixed point of the Dirichlet beta function. 0
7, 2, 6, 5, 6, 4, 1, 9, 3, 2, 7, 4, 0, 4, 3, 6, 2, 6, 4, 4, 1, 6, 2, 4, 1, 3, 0, 1, 0, 1, 1, 3, 3, 4, 1, 5, 5, 0, 4, 3, 3, 0, 8, 4, 7, 2, 3, 9, 1, 2, 0, 0, 2, 2, 4, 2, 0, 2, 8, 4, 1, 0, 3, 4, 6, 4, 5, 4, 3, 1, 7, 4, 8, 1, 3, 3, 2, 2, 0, 8, 1, 3, 2, 2, 2, 0, 2, 4, 6, 5, 7, 6, 3, 4, 1, 0, 2, 0, 7, 9, 6, 3, 4, 0, 5, 5, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..106.

Eric Weisstein's MathWorld, Dirichlet Beta Function.

Wikipedia, Dirichlet beta function.

EXAMPLE

0.72656419327404362644162413010113341550433084723912002242028410346454317481...

MAPLE

Digits:= 140:

f:= s-> sum((-1)^n/(2*n+1)^s, n=0..infinity):

fsolve(f(x)=x, x);  # Alois P. Heinz, Feb 05 2018

MATHEMATICA

RealDigits[ FindRoot[ DirichletBeta[x] == x, {x, 0}, WorkingPrecision -> 2^7, AccuracyGoal -> 2^8, PrecisionGoal -> 2^7][[1, 2]], 10, 111][[1]] (* Robert G. Wilson v, Jan 07 2018 *)

PROG

(PARI) solve(x=0, 1, sumalt(n=0, ((-1)^n)/(2*n+1)^x)-x)

CROSSREFS

Cf. A261624.

Sequence in context: A225444 A175408 A019934 * A182548 A322933 A143306

Adjacent sequences:  A295871 A295872 A295873 * A295875 A295876 A295877

KEYWORD

nonn,cons

AUTHOR

Michal Paulovic, Dec 31 2017

STATUS

approved

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Last modified August 4 13:38 EDT 2020. Contains 336201 sequences. (Running on oeis4.)