A335263 Decimal expansion of -(Pi/8 + EulerGamma/4 + log(8*Pi)/4 - 2).

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

Offset

0,1

Comments

Conjecture: Equals -(1/Pi)*Integral_{t=0..Infinity} log(|Zeta(1/2 + i*t)/Zeta(1/2)|) *(1/t^2) dt. The Riemann hypothesis is equivalent to this conjecture.

Links

Table of n, a(n) for n=0..87.

Milin, Answer to: Collection of equivalent forms of Riemann Hypothesis, version: 2019-07-18, MathOverflow.

Example

Equals 0.656954145193583604441760625637564427746365187094111539207774...

Maple

Digits := 120: -(Pi/8 + gamma/4 + log(8*Pi)/4 - 2)*10^88:
ListTools:-Reverse(convert(floor(%), base, 10));

Mathematica

RealDigits[-(Pi/8+EulerGamma/4+Log[8*Pi]/4-2), 10, 120][[1]] (* Harvey P. Dale, Sep 28 2021 *)

Prog

(PARI) -(Pi/8 + Euler/4 + log(8*Pi)/4 - 2) \\ Michel Marcus, Jun 12 2020

Crossrefs

Sequence in context: A023408 A133616 A019621 * A126689 A243093 A101634

Adjacent sequences: A335260 A335261 A335262 * A335264 A335265 A335266

Keyword

nonn,cons

Author

Peter Luschny, Jun 11 2020

Status

approved