A351829 Decimal expansion of (4/3)*Pi*Sum_{k>=1} 1/k^(3/2).

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

Offset

2,3

Comments

Total volume of an infinite stack of spheres having radii 1, 1/sqrt(2), 1/sqrt(3), ...

Both the height and the surface area of the stack are infinite, while the volume converges to this constant. See the linked YouTube video (where the constant is given with a lower precision).

Links

Paolo Xausa, Table of n, a(n) for n = 2..10000

Michael Penn, An infinite stack of spheres paradox, YouTube video, 2022.

Formula

Equals (4/3)*Pi*zeta(3/2) = (4/3)*A000796*A078434.

Example

10.942692271799206272216256897081299599642276797641827117794965018259...

Mathematica

nterms=100; First[RealDigits[4/3*Pi*Zeta[3/2], 10, nterms]]

Prog

(PARI) 4/3*Pi*zeta(3/2) \\ Michel Marcus, Feb 21 2022

Crossrefs

Cf. A000796, A078434.

Sequence in context: A039663 A155535 A099879 * A126774 A179587 A223709

Adjacent sequences: A351826 A351827 A351828 * A351830 A351831 A351832

Keyword

nonn,cons

Author

Paolo Xausa, Feb 21 2022

Status

approved