OFFSET
0,2
COMMENTS
Equivalently, the real number in (0,1) having the characteristic function of the primes, A010051, as its base-4 expansion. - M. F. Hasler, Jul 04 2017
FORMULA
Equals 3 * Sum_{k>=1} pi(k)/4^(k+1), where pi(k) = A000720(k). - Amiram Eldar, Aug 11 2020
EXAMPLE
0.079162851037850149671771117962208184613038569751878...
PROG
(PARI) /* Sum of 1/m^p for primes p */ sumnp(n, m) = { local(s=0, a, j); for(x=1, n, s+=1./m^prime(x); ); a=Vec(Str(s)); for(j=3, n, print1(eval(a[j])", ") ) }
(PARI) suminf(n=1, 1/4^prime(n)) \\ Then: digits(%\.1^default(realprecision))[1..-3] to remove the last 2 digits. N.B.: Functions sumpos() and sumnum() yield much less accurate results. - M. F. Hasler, Jul 04 2017
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Cino Hilliard, Nov 17 2007
EXTENSIONS
Offset corrected R. J. Mathar, Jan 26 2009
Edited by M. F. Hasler, Jul 04 2017
STATUS
approved