A391785 Decimal expansion of zeta(2) * Product_{p prime} (1 - 2/p^2 + 1/p^(2/5) - 1/p^(3/2) + 1/p^4).

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

Offset

0,1

Links

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

Hendrik Jager, The avarage order of Gaussian sums (sic), Studies in Pure Mathematics: To the Memory of Paul Turán, Basel: Birkhäuser Basel, 1983, pp. 381-384.

Example

0.763356430216229590099944391673209107742458366621501...

Mathematica

res[m_, dig_] := Block[{$MaxExtraPrecision = 2*dig, ps = {2, 3, 5}, c = LinearRecurrence[{0, 0, 0, 2, -1, 0, 1, -1}, {0, 0, 0, -8, 5, 0, -7, -8}, m]}, RealDigits[Zeta[2] * Product[(1 - 2/p^2 + 1/p^(5/2) - 1/p^(7/2) + 1/p^4), {p, ps}] * Exp[NSum[Indexed[c, n]*(PrimeZetaP[n/2] - Sum[1/p^(n/2), {p, ps}])/n, {n, 4, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, dig][[1]]]; With[{dig = 120}, res[FixedPoint[# + 100 &, 10, SameTest -> (Equal[res[#1, dig], res[#2, dig]] &)], dig]]

Prog

(PARI) zeta(2) * prodeulerrat(1 - 2/p^4 + 1/p^5 - 1/p^7 + 1/p^8, 1/2)

Crossrefs

Cf. A013661.

Sequence in context: A291081 A030797 A019908 * A021135 A198374 A225450

Adjacent sequences: A391782 A391783 A391784 * A391786 A391787 A391788

Keyword

nonn,cons

Author

Amiram Eldar, Dec 20 2025

Status

approved