

A338858


Decimal expansion of Sum_{k>=0} (zeta(4*k+3)1).


2



2, 1, 0, 9, 3, 2, 9, 9, 2, 7, 6, 2, 0, 0, 4, 9, 1, 8, 9, 3, 9, 1, 9, 5, 2, 8, 6, 4, 0, 2, 1, 5, 6, 5, 7, 6, 7, 5, 9, 2, 1, 1, 1, 5, 3, 8, 5, 1, 7, 3, 2, 6, 1, 1, 0, 1, 9, 3, 7, 8, 4, 7, 9, 5, 0, 1, 8, 8, 6, 4, 2, 0, 7, 6, 8, 4, 7, 2, 6, 6, 2, 1, 6, 0, 2, 0, 8, 8, 8, 6, 3, 9, 3, 6, 0, 0, 2, 1, 0, 6, 6, 4, 1, 9, 8
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OFFSET

0,1


COMMENTS

For additional comments and generalization see A339604.


LINKS

Table of n, a(n) for n=0..104.


FORMULA

Equals Sum_{k>=2} k/(k^41).
Equals 1/8 + gamma/2 + Re(Psi(i))/2, where Psi is the digamma function, gamma is the EulerMascheroni constant (see A001620), and i=sqrt(1).
Equals 1/8 + Re(H(I))/2, where H is the harmonic number function.


EXAMPLE

0.2109329927620049189391952864...


MATHEMATICA

RealDigits[N[Re[Sum[Zeta[4 n + 3]  1, {n, 0, Infinity}]], 105]][[1]]


PROG

(PARI) suminf(k=0, zeta(4*k+3)1) \\ Michel Marcus, Dec 24 2020


CROSSREFS

Cf. A256919 (4*k), A339097 (4*k+1), A339083 (4k+2).
Cf. A024006, A338815, A339135, A339529, A339530, A339604, A339605, A339606.
Sequence in context: A322222 A265012 A285285 * A201897 A246658 A274740
Adjacent sequences: A338855 A338856 A338857 * A338859 A338860 A338861


KEYWORD

nonn,cons


AUTHOR

Artur Jasinski, Dec 24 2020


STATUS

approved



