A387289 - OEIS

A387289

Decimal expansion of Sum_{n>=1} (-1)^(n+1) P(3*n)/(3*n), where P(x) is the prime zeta function.

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

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..105.

FORMULA

Equals log(zeta(3)/zeta(6))/3.

Equals log(3*(35*zeta(3))^(1/3)/Pi^2).

Sum_{p prime} Sum_{n>=1} (-1)^(n+1)/p^(3*n)/(3*n) = Sum_{p prime} log((1+1/p^3))/3 = log(Product_{p prime} (1+1/p^3))/3 = log(zeta(3)/zeta(6))/3. - Amiram Eldar, Aug 25 2025

EXAMPLE

0.055613262596277710178747463453...

MATHEMATICA

RealDigits[Log[Zeta[3]/Zeta[6]]/3, 10, 105, -1][[1]]

CROSSREFS

Cf. A387293.

Sequence in context: A224093 A193555 A390906 * A161981 A346962 A258072

Adjacent sequences: A387286 A387287 A387288 * A387290 A387291 A387292

KEYWORD

nonn,cons

AUTHOR

Artur Jasinski, Aug 25 2025

STATUS

approved