A369508 Decimal expansion of Sum_{n>=1} prime(n)*(-1/2)^n (negated).

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

Offset: 0

Author

Pierluigi Failla, Jan 25 2024

Keywords

• nonn
• cons

Examples

			0.662729784185267965388337694463998...
		

Crossrefs

Cf. A098990.

Programs

Mathematica

First[RealDigits[Sum[Prime[n](-2)^-n,{n,1000}],10,85]] (* James C. McMahon, Jan 29 2024 *)

PARI

suminf(k=1, prime(k)/(-2)^k) \\ Michel Marcus, Jan 25 2024

Python

from sympy import prime
from decimal import Decimal, getcontext
getcontext().prec = 100
def f(k):
    if k == 1:
        return prime(k) * Decimal(-0.5)
    return f(k-1) + prime(k) * Decimal(-0.5) ** k