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

Author

Stanislav Sykora, Nov 14 2014

Keywords

• nonn
• cons
• easy

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)).

Examples

			0.9235638316741813823235099539877039168469319632611163252035958316...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 0..2000
• Eric Weisstein's World of Mathematics, Mertens Theorem, Equations 5-9

Crossrefs

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

Programs

Magma

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

Mathematica

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

PARI

Pi^2/6/exp(Euler)

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