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%I #11 Aug 11 2020 09:59:46
%S 0,7,9,1,6,2,8,5,1,0,3,7,8,5,0,1,4,9,6,7,1,7,7,1,1,1,7,9,6,2,2,0,8,1,
%T 8,4,6,1,3,0,3,8,5,6,9,7,5,1,8,7,8,0,8,4,1,7,9,0,9,9,9,1,5,2,3,1,2,0,
%U 9,6,3,2,6,6,1,3,8,1,7,1,1,5,8,2,7,8,0,6,7,0,3,6,0,2,2,2,0,6
%N Decimal expansion of Sum_{n >= 1} 1/4^prime(n).
%C 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
%F Equals 3 * Sum_{k>=1} pi(k)/4^(k+1), where pi(k) = A000720(k). - _Amiram Eldar_, Aug 11 2020
%e 0.079162851037850149671771117962208184613038569751878...
%o (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])",") ) }
%o (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
%Y Cf. A000720, A051006 (analog for base 2), A132800 (analog for base 3), A132797 (analog for base 5), A010051 (characteristic function of the primes), A000040 (the primes).
%K cons,nonn
%O 0,2
%A _Cino Hilliard_, Nov 17 2007
%E Offset corrected _R. J. Mathar_, Jan 26 2009
%E Edited by _M. F. Hasler_, Jul 04 2017
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