A354952 Decimal expansion of Sum_{p primes} 1/(p*log(p) - 1).

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

Offset: 1

Author

Vaclav Kotesovec, Jun 13 2022

Keywords

• nonn
• cons
• more

Examples

			3.663504585465603301602825244808212333209344522564373994...
		

Crossrefs

Cf. A137245, A319232, A137250.

Programs

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.

Formula

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