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Decimal expansion of Sum_{p primes} 1/(p*log(p) - 1).
5

%I #16 Jun 24 2022 01:13:53

%S 3,6,6,3,5,0,4,5,8,5,4,6,5,6,0,3,3,0,1,6,0,2,8,2,5,2,4,4,8,0,8,2,1,2,

%T 3,3,3,2,0,9,3,4,4,5,2,2,5,6,4,3,7,3,9,9,4

%N Decimal expansion of Sum_{p primes} 1/(p*log(p) - 1).

%F Equals Sum_{k>=1} (Sum_{p primes} 1/(p*log(p))^k).

%e 3.663504585465603301602825244808212333209344522564373994...

%o (PARI) prec = 60; tot = 0; dif = 10^(-prec); for(s=1, 200, default(realprecision, 200 + 6*s); su = 0; d = 0; k = 0; while(abs(d)>dif || exponent(d)==-oo, k=k+1; d = moebius(k) / ((s-1)! * k^(s+1)) * intnum(x=s*k, [[1], 1], (x-s*k)^(s-1) * log(zeta(x))); su = su + d; ); tot = tot + su; print(tot);); \\ It takes several hours.

%Y Cf. A137245, A319232, A137250.

%K nonn,cons,more

%O 1,1

%A _Vaclav Kotesovec_, Jun 13 2022