cp's OEIS Frontend

A152419 Decimal expansion of 3-Pi^2/6-zeta(3).

%I A152419 #19 Jul 01 2022 17:27:26
%S A152419 1,5,3,0,0,9,0,2,9,9,9,2,1,7,9,2,7,8,1,2,7,8,4,6,6,7,1,8,4,2,5,2,4,8,
%T A152419 2,0,0,1,6,0,6,3,8,0,6,4,5,2,7,0,2,6,8,0,4,7,2,1,7,0,2,1,5,2,8,8,1,5,
%U A152419 4,3,2,3,8,1,0,4,8,6,0,3,5,9,7,9,9,1,5,2,2,5,7,7,0,9,0,6,0,3,6,5,4,9,7,9,6
%N A152419 Decimal expansion of 3-Pi^2/6-zeta(3).
%C A152419 Consider the constants N(s) = Sum_{n>=2} 1/(n^s*(n-1)) = s-Sum_{k=2..s} zeta(k), where zeta() is Riemann's zeta function. We have N(1)=1 and this constant here is N(3).
%H A152419 R. J. Mathar, <a href="http://arxiv.org/abs/0803.0900">Series of reciprocal powers of k-almost primes</a>, arXiv:0803.0900 [math.NT], 2008-2009, section 4.1.
%F A152419 Equals 3-A013661-A002117.
%e A152419 0.15300902999217927812784667184252482001606380645270268047217021528815...
%p A152419 evalf(3-Pi^2/6-Zeta(3));
%t A152419 RealDigits[3-Pi^2/6-Zeta[3],10,120][[1]] (* _Harvey P. Dale_, Jul 01 2022 *)
%o A152419 (PARI) 3-Pi^2/6-zeta(3) \\ _Charles R Greathouse IV_, Jan 31 2017
%o A152419 (Sage) t(n) = 1/(n*(n+1)^(3));
%o A152419 sum(t(n), n, 1, oo).n(digits=107); # _Jani Melik_, Nov 20 2020
%Y A152419 Cf. A013661 (Pi^2/6), A002117 (zeta(3)).
%Y A152419 Cf. A152416.
%K A152419 cons,easy,nonn
%O A152419 0,2
%A A152419 _R. J. Mathar_, Dec 03 2008