A182448 Decimal expansion of Pi^2/15.

6, 5, 7, 9, 7, 3, 6, 2, 6, 7, 3, 9, 2, 9, 0, 5, 7, 4, 5, 8, 8, 9, 6, 6, 0, 6, 6, 6, 5, 8, 4, 1, 0, 0, 7, 5, 6, 8, 7, 5, 7, 9, 9, 6, 0, 4, 8, 2, 7, 1, 9, 3, 7, 5, 0, 9, 4, 2, 2, 3, 2, 9, 1, 7, 4, 8, 0, 0, 2, 9, 8, 8, 1, 6, 1, 2, 8, 0, 3, 4, 9, 5, 3, 3, 4, 5, 1, 5, 6, 0, 2, 4, 7, 9, 0, 3, 4, 8, 2, 1, 2, 1, 6, 0, 1

Offset

0,1

Links

Table of n, a(n) for n=0..104.

László Tóth, Linear combinations of Dirichlet series associated with the Thue-Morse sequence, Integers: Electronic Journal of Combinatorial Number Theory, Vol. 22 (2022), #A98; arXiv preprint, arXiv:2211.13570 [math.NT], 2022.

Index entries for transcendental numbers.

Formula

See Mathematica code.

Equals Gamma(4)*zeta(4)/Pi^2 = zeta(4)/zeta(2) = A013662/A013661 = Product_{p prime} (p^2/(p^2+1)). - Stanislav Sykora, Oct 21 2014

Equals (1/10) * Sum_{n >= 0} (-1)^n*( 1/(n + 1/3)^2 - 1/(n + 2/3)^2 ). - Peter Bala, Oct 31 2019

Equals Sum_{k>=1} A008836(k)/k^2. - Amiram Eldar, Jun 23 2020

Equals (1/10) * Sum_{k>=1} (5*t(k-1) + 3*t(k))/k^2, where t(k) = A010060(k) (Tóth, 2022). - Amiram Eldar, Feb 04 2024

Example

0.65797362673929...

Mathematica

RealDigits[N[Sum[1/(n + 0)^2 - 1/(n + 1)^2 + 1/(n + 2)^2 - 1/(n + 3)^2 - 4/(n + 4)^2 - 1/(n + 5)^2 + 1/(n + 6)^2 - 1/(n + 7)^2 + 1/(n + 8)^2 + 4/(n + 9)^2, {n, 1, Infinity, 10}], 90]][[1]]
RealDigits[N[Sum[LiouvilleLambda[n]/n^2, {n, 1, Infinity}], 90]][[1]]
RealDigits[Pi^2/15, 10, 120][[1]] (* Harvey P. Dale, May 28 2017 *)

Prog

(PARI) Pi^2/15 \\ Michel Marcus, Oct 21 2014

Crossrefs

Cf. A000796, A008836, A010060, A013661, A013662, A086463, A191898, A249103.

Cf. A347328, A347329, A347330, A347331.

Sequence in context: A245535 A191102 A021156 * A179591 A063046 A104909

Adjacent sequences: A182445 A182446 A182447 * A182449 A182450 A182451

Keyword

nonn,cons

Author

Mats Granvik, Apr 29 2012

Extensions

Offset corrected and more terms added by Rick L. Shepherd, Jan 08 2014

Status

approved