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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
OFFSET
0,1
LINKS
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
KEYWORD
nonn,cons
AUTHOR
Michal Paulovic, Dec 31 2017
STATUS
approved