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

0,2

Links

Table of n, a(n) for n=0..99.

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)

Example

0.17063498029777667950378075569138458326845152372416604426350917102271807...

Prog

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

Crossrefs

Cf. A010051, A065855, A119523, A275306.

Sequence in context: A153871 A365350 A198934 * A260799 A021590 A094241

Adjacent sequences: A119521 A119522 A119523 * A119525 A119526 A119527

Keyword

nonn,cons

Author

Roger L. Bagula, May 27 2006

Extensions

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

Better name from Joerg Arndt, Jan 16 2024

Status

approved