A395220 Entropy of the zeta probability distribution with parameter s=4.

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

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 = 4.

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^4/zeta(4))/k^4/zeta(4)).

Equals log(zeta(4))-4*zeta'(4)/zeta(4).

Example

0.33378893288882013575...

Prog

(PARI) \p200
s=4; zs=zeta(s);
a=log(zs)-(s/zs)*zeta'(s);
precision(a, 105)

Crossrefs

Cf. A395218 (s=2), A395219 (s=3).

Cf. A013661, A073002.

Sequence in context: A031503 A049500 A227826 * A268127 A200076 A342335

Adjacent sequences: A395217 A395218 A395219 * A395221 A395222 A395224

Keyword

nonn,cons

Author

Stanislav Sykora, Apr 18 2026

Status

approved