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A363368
Decimal expansion of Sum_{primes p} 1/(p*log(p)*log(log(p))).
3
1, 9, 0, 6, 9, 7, 3, 8, 4, 8, 0, 3, 4, 9, 5, 4, 4, 1, 7, 7, 8, 7, 5, 7, 9, 6, 6, 9, 6, 5, 1, 9, 6, 4, 0, 3, 3, 6, 1, 8, 9, 3, 8, 3, 5, 2, 2, 9, 4, 8, 5, 3, 6, 6, 0, 5, 5, 9, 5, 2, 4, 2, 9, 4, 7, 1, 4, 5, 6, 7, 8, 3, 1, 2, 9, 2, 5, 2, 2, 4, 4, 1, 0, 9, 2, 3, 1, 8, 7, 1, 9, 4, 1, 3, 3, 4, 1, 6, 4, 8, 2, 2, 4, 2, 3
OFFSET
1,2
COMMENTS
Value computed and communicated by Bill Allombert and confirmed by Pascal Sebah.
EXAMPLE
1.9069738480349544...
PROG
(PARI) /* author Bill Allombert */
\p150
pz(x, ex=0)=
{
my(s=bitprecision(x));
my(B=s/real(polcoef(x, 0))+ex);
sum(n=1, B, my(a=moebius(n)); if(a!=0, a*log(zeta(n*x))/n));
}
my(P=primes([2, 61])); intnum(x=1, [oo, log(67)], (pz(x)-vecsum([p^-x|p<-P]))*intnum(s=0, [oo, 1], (x-1)^s/gamma(1+s))) + vecsum([1/p/log(p)/log(log(p))|p<-P])
KEYWORD
nonn,cons
AUTHOR
Artur Jasinski, Jun 11 2023
STATUS
approved