A397824 Decimal expansion of Product_{p prime} (1-1/p)^9 * (1 + 9/p + 9/p^2 + 1/p^3).

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

Offset

0,4

Comments

This constant, c, appears in the conjectured asymptotic formula for the eighth power moment of the Riemann zeta function on the critical line: Integral_{t=0..T} |zeta(1/2 + i*t)|^8 dt ~ (24024/16!) * c * T * log(T)^16 (Keating and Snaith, 1998; Conrey and Gonek, 2001).

References

Jonathan Keating and Nina Snaith, Random matrix theory and some zeta-function moments, lecture at Erwin Schrodinger Institute, Vienna, Sept. 1998.

Links

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

Alain Connes, The Riemann Hypothesis: Past, Present and a Letter Through Time, arXiv:2602.04022 [math.NT], 2026. See pp. 17-18.

John Brian Conrey and Steven Mark Gonek, High moments of the Riemann zeta-function, Duke Math. J., Vol. 107, No. 3 (2001), pp. 577-604; alternative link.

Example

0.000214681409775622181339642850420901783265945992138...

Prog

(PARI) prodeulerrat((1-1/p)^9 * (1 + 9/p + 9/p^2 + 1/p^3))

Crossrefs

Cf. A397823.

Sequence in context: A111104 A026190 A378342 * A262599 A160016 A245089

Adjacent sequences: A397819 A397820 A397823 * A397826 A397828 A397830

Keyword

nonn,cons

Author

Amiram Eldar, Jul 11 2026

Status

approved