This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A383432 #17 May 20 2025 10:41:39
%S A383432 0,3,7,1,6,7,3,4,3,5,4
%N A383432 Decimal expansion of the multiple prime zeta value p[2, 1, 1].
%C A383432 Prime multiple zeta constants p[m,...,n] are equivalents of multiple zeta constants when successive natural numbers are replaced by successive primes.
%C A383432 For complete list of multiple prime zeta values up to weight 6 see A382234.
%F A383432 Equals Sum_{p,q,r prime p>q>r} 1/(p^2*q*r).
%F A383432 Equals (p[2, 1, 3] + p[2, 3, 1] + p[4, 1, 1] + p[2, 1, 1, 2] + p[2, 1, 2, 1] + 2 p[2, 2, 1, 1])/p[2].
%F A383432 Equals (p[2] p[4] + p[2, 1]^2 + p[2] p[2, 2] + p[2, 4] + p[2, 1, 3] + p[2, 2, 2] - p[2, 3, 1] - p[4, 1, 1] + p[2, 1, 1, 2] - p[2, 1, 2, 1] - 2 p[2, 2, 1, 1] - p[2]^3)/p[2].
%e A383432 0.03716734354...
%o A383432 (PARI)
%o A383432 f(e)=my(S=sumeulerrat(1/x^2),u=0.,v=0,w=0.);forprime(p=2,prime(2^e),u+=v*S;S-=1/p^2;v=w/p;w+=1/p);u;
%o A383432 f(30) \\ Bill Allombert
%Y A383432 Cf. A085548, A085541, A085965, A382234, A382235, A382236, A382634, A382635, A382636, A382637.
%K A383432 nonn,cons,more
%O A383432 0,2
%A A383432 _Artur Jasinski_, Apr 27 2025