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

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, 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, 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

Offset: 0

Author

R. J. Mathar, Dec 03 2008

Keywords

• cons
• easy
• nonn

Comments

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).

Examples

			0.15300902999217927812784667184252482001606380645270268047217021528815...
		

Links

• R. J. Mathar, Series of reciprocal powers of k-almost primes, arXiv:0803.0900 [math.NT], 2008-2009, section 4.1.

Crossrefs

Cf. A013661 (Pi^2/6), A002117 (zeta(3)).

Cf. A152416.

Programs

Maple

evalf(3-Pi^2/6-Zeta(3));

Mathematica

RealDigits[3-Pi^2/6-Zeta[3],10,120][[1]] (* Harvey P. Dale, Jul 01 2022 *)

PARI

3-Pi^2/6-zeta(3) \\ Charles R Greathouse IV, Jan 31 2017

Sage

t(n) = 1/(n*(n+1)^(3));
sum(t(n), n, 1, oo).n(digits=107); # Jani Melik, Nov 20 2020

Formula

Equals 3-A013661-A002117.