cp's OEIS Frontend

A336405 Decimal expansion of Sum_{n>=1} log(n*sin(1/n)) (negated).

%I A336405 #30 Jul 30 2023 02:26:24
%S A336405 2,8,0,5,5,6,3,3,6,2,2,9,1,5,5,0,7,9,6,0,2,0,3,9,6,8,0,9,3,9,1,9,8,3,
%T A336405 6,2,1,7,4,5,0,2,8,2,9,4,5,9,7,1,5,1,5,5,9,0,4,7,7,3,8,5,3,7,9,5,1,5,
%U A336405 6,7,7,2,1,0,9,9,9,1,1,6,9,0,7,4,2,7,7
%N A336405 Decimal expansion of Sum_{n>=1} log(n*sin(1/n)) (negated).
%C A336405 As v(n) = log(n*sin(1/n)) ~ -1/(6*n^2) when n -> oo, this series is convergent (zeta(2)/6 ~ 0.2741556778...).
%F A336405 Equals Sum_{n>=1} log(n*sin(1/n)).
%F A336405 Equals log(A295219).
%F A336405 From _Amiram Eldar_, Jul 30 2023: (Start)
%F A336405 Equals Sum_{k>=1} 2^(2*k-1)*(-1)^k*B(2*k)*zeta(2*k)/(k*(2*k)!), where B(k) is the k-th Bernoulli number.
%F A336405 Equals -Sum_{k>=1} zeta(2*k)^2/(k*Pi^(2*k)). (End)
%e A336405 -0.28055633622915507960203968093919836217450282945971...
%p A336405 evalf(sum(log(n*sin(1/n)),n=1..infinity),50);
%o A336405 (PARI) sumpos(n=1, log(n*sin(1/n))) \\ _Michel Marcus_, Jul 20 2020
%Y A336405 Cf. A013661, A233383, A248945, A295219, A336603.
%Y A336405 Cf. A027641, A027642.
%K A336405 nonn,cons
%O A336405 0,1
%A A336405 _Bernard Schott_, Jul 20 2020
%E A336405 More terms from _Jinyuan Wang_, Jul 21 2020