A363368 - OEIS

A363368

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

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Value computed and communicated by Bill Allombert and confirmed by Pascal Sebah.

LINKS

Table of n, a(n) for n=1..105.

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])

CROSSREFS

Cf. A077761, A086242, A137245, A138312, A221711, A303493, A319231, A319232, A354887, A354917, A354952, A361972, A362533.

Sequence in context: A296566 A198213 A093766 * A097674 A372830 A309823

Adjacent sequences: A363365 A363366 A363367 * A363369 A363370 A363371

KEYWORD

nonn,cons

AUTHOR

Artur Jasinski, Jun 11 2023

STATUS

approved