A246499 Decimal expansion of zeta(2)/exp(gamma), gamma being the Euler-Mascheroni constant.

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

Offset

0,1

Comments

It follows from Mertens theorem that this constant is the limit for large m of log(prime(m))*Product_{k=1..m} 1/(1 + 1/prime(k)).

Links

Stanislav Sykora, Table of n, a(n) for n = 0..2000

Eric Weisstein's World of Mathematics, Mertens Theorem, Equations 5-9

Formula

Equals Pi^2/(6*exp(gamma)).

Equals lim_{m->infinity} log(prime(m))*Product_{k=1..m} 1/(1 + 1/prime(k)).

Equals A013661/A073004. - Michel Marcus, Nov 18 2014

Example

0.9235638316741813823235099539877039168469319632611163252035958316...

Mathematica

RealDigits[Zeta[2]/E^EulerGamma, 10, 100][[1]] (* Alonso del Arte, Nov 14 2014 *)

Prog

(PARI) Pi^2/6/exp(Euler)
(Magma) R:=RealField(100); Pi(R)^2/(6*Exp(EulerGamma(R))); // G. C. Greubel, Aug 30 2018

Crossrefs

Cf. A001113, A000796, A001620, A013661, A073004, A080130, A097663.

Sequence in context: A104539 A201559 A300015 * A199002 A160108 A011344

Adjacent sequences: A246496 A246497 A246498 * A246500 A246501 A246502

Keyword

nonn,cons,easy

Author

Stanislav Sykora, Nov 14 2014

Status

approved