A395220 - OEIS

%I #17 Apr 30 2026 00:24:50

%S 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,

%T 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,

%U 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

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

%C 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.

%H Stanislav Sykora, <a href="/A395220/b395220.txt">Table of n, a(n) for n = 0..999</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Zeta_distribution">Zeta distribution</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Entropy_(information_theory)">Entropy (information theory)</a>.

%F Equals -Sum_{k>=1} (log(1/k^4/zeta(4))/k^4/zeta(4)).

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

%e 0.33378893288882013575...

%o (PARI) \p200

%o s=4; zs=zeta(s);

%o a=log(zs)-(s/zs)*zeta'(s);

%o precision(a, 105)

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

%Y Cf. A013661, A073002.

%K nonn,cons

%O 0,1

%A _Stanislav Sykora_, Apr 18 2026