cp's OEIS Frontend

A382635 Decimal expansion of the multiple prime zeta value p[3, 2].

%I A382635 #29 Apr 27 2025 00:37:29
%S A382635 0,1,4,0,9,5,7,6,8,7,5,4,8,0,3,8,3,3,5,1,2,7,2,0,3,1,3,5,9,9,8,7,9,9,
%T A382635 7,4,8,8,5
%N A382635 Decimal expansion of the multiple prime zeta value p[3, 2].
%C A382635 Prime multiple zeta constants p[m,...,n] are equivalents of multiple zeta constants when successive natural numbers are replaced by successive primes.
%C A382635 For complete list of multiple prime zeta values up to weight 6 see A382234.
%F A382635 Equals Sum_{p,q prime p>q} 1/(p^3*q^2).
%F A382635 Equals A085548*A085541 - A085965 - A382634.
%F A382635 For partial sums and in infinity occurs identity:
%F A382635 p[2, 3] + p[3, 2] + p[2, 1, 2] + p[2, 2, 1] = p[1]*p[2, 2] - p[1, 2, 2]
%F A382635 where p[1] and p[1, 2, 2] are divergent series then
%F A382635 lim_{n->oo} p[1](n)*A382234 - p[1, 2, 2](n) = 0.067101047034256...
%e A382635 0.014095768754803833512720313599879974885...
%t A382635 p3 = N[PrimeZetaP[3], 50]; p = 2; sum = 0; sum1 = 0; diff = 0; Monitor[Do[sum = sum + N[1/p^3, 50]; diff = p3 - sum; sum1 = sum1 + diff/p^2; p = NextPrime[p], {n, 1, 100000000}], {sum1, n}]
%Y A382635 Cf. A085548, A085541, A085965, A382234, A382235, A382236, A382634.
%Y A382635 Cf. A258983.
%K A382635 nonn,cons,more
%O A382635 0,3
%A A382635 _Artur Jasinski_, Apr 01 2025