|
%I #34 Feb 25 2022 17:53:40
%S 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,
%T 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,
%U 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
%N Decimal expansion of zeta(2)/exp(gamma), gamma being the Euler-Mascheroni constant.
%C 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)).
%H Stanislav Sykora, <a href="/A246499/b246499.txt">Table of n, a(n) for n = 0..2000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MertensTheorem.html">Mertens Theorem</a>, Equations 5-9
%F Equals Pi^2/(6*exp(gamma)).
%F Equals lim_{m->infinity} log(prime(m))*Product_{k=1..m} 1/(1 + 1/prime(k)).
%F Equals A013661/A073004. - _Michel Marcus_, Nov 18 2014
%e 0.9235638316741813823235099539877039168469319632611163252035958316...
%t RealDigits[Zeta[2]/E^EulerGamma, 10, 100][[1]] (* _Alonso del Arte_, Nov 14 2014 *)
%o (PARI) Pi^2/6/exp(Euler)
%o (Magma) R:=RealField(100); Pi(R)^2/(6*Exp(EulerGamma(R))); // _G. C. Greubel_, Aug 30 2018
%Y Cf. A001113, A000796, A001620, A013661, A073004, A080130, A097663.
%K nonn,cons,easy
%O 0,1
%A _Stanislav Sykora_, Nov 14 2014
|
