A119524 Decimal expansion of Sum_{k >= 1} ((-1)^A010051(k))/2^k.

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, 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, 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

Offset: 0

Author

Roger L. Bagula, May 27 2006

Keywords

• nonn
• cons

Examples

			0.17063498029777667950378075569138458326845152372416604426350917102271807...
		

Crossrefs

Cf. A010051, A065855, A119523, A275306.

Programs

PARI

suminf(k=1, (-1)^isprime(k)/2^k) \\ Michel Marcus, Jan 16 2024

Formula

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

From Antonio Graciá Llorente, Jan 14 2024: (Start)

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

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

Equals 2*A275306. (End)

Extensions

Edited and corrected by N. J. A. Sloane, Nov 17 2006

Better name from Joerg Arndt, Jan 16 2024