A119524 - OEIS

%I #57 Jan 21 2024 06:31:01

%S 1,7,0,6,3,4,9,8,0,2,9,7,7,7,6,6,7,9,5,0,3,7,8,0,7,5,5,6,9,1,3,8,4,5,

%T 8,3,2,6,8,4,5,1,5,2,3,7,2,4,1,6,6,0,4,4,2,6,3,5,0,9,1,7,1,0,2,2,7,1,

%U 8,0,7,8,7,6,1,2,8,5,3,3,1,6,0,7,4,1,9,9,0,3,1,4,3,0,4,8,4,4,4,1

%N Decimal expansion of Sum_{k >= 1} ((-1)^A010051(k))/2^k.

%F Equals Sum_{k >= 1} (k - 1 - PrimePi(k))/2^k = Sum_{k >= 1} A065855(k)/2^k.

%F From _Antonio Graciá Llorente_, Jan 14 2024: (Start)

%F Equals Sum_{k >= 2} A005171(k)/2^(k-1).

%F Equals Sum_{k >= 1} ((-1)^A010051(k))/2^k.

%F Equals 2*A275306. (End)

%e 0.17063498029777667950378075569138458326845152372416604426350917102271807...

%o (PARI) suminf(k=1, (-1)^isprime(k)/2^k) \\ _Michel Marcus_, Jan 16 2024

%Y Cf. A010051, A065855, A119523, A275306.

%K nonn,cons

%O 0,2

%A _Roger L. Bagula_, May 27 2006

%E Edited and corrected by _N. J. A. Sloane_, Nov 17 2006

%E Better name from _Joerg Arndt_, Jan 16 2024