A395219 Entropy of the zeta probability distribution with parameter s=3.

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

Offset

0,1

Comments

Sum_{k>=1} (-m(k)*log(m(k))), where m(k) is the mass distribution function for zeta distribution, m(k) = 1/k^s/zeta(s), with s = 3.

Links

Stanislav Sykora, Table of n, a(n) for n = 0..999

Wikipedia, Zeta distribution.

Wikipedia, Entropy (information theory).

Formula

Equals -Sum_{k>=1} (log(1/k^3/zeta(3))/k^3/zeta(3)).

Equals log(zeta(3))-3*zeta'(3)/zeta(3).

Example

0.678502221866323142064...

Prog

(PARI) \p200
s=3; zs=zeta(s);
a=log(zs)-(s/zs)*zeta'(s);
precision(a, 105)

Crossrefs

Cf. A395218 (s=2), A395220 (s=4).

Cf. A013661, A073002.

Sequence in context: A117022 A051994 A085661 * A382591 A265276 A286474

Adjacent sequences: A395216 A395217 A395218 * A395220 A395221 A395222

Keyword

nonn,cons

Author

Stanislav Sykora, Apr 18 2026

Status

approved