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

%I A369508 #17 Feb 24 2024 14:16:37
%S A369508 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,
%T A369508 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,
%U A369508 0,6,1,1,9,9,4,2,0,8,2,6,6,8,8,1,5
%N A369508 Decimal expansion of Sum_{n>=1} prime(n)*(-1/2)^n  (negated).
%e A369508 0.662729784185267965388337694463998...
%t A369508 First[RealDigits[Sum[Prime[n](-2)^-n,{n,1000}],10,85]] (* _James C. McMahon_, Jan 29 2024 *)
%o A369508 (Python)
%o A369508 from sympy import prime
%o A369508 from decimal import Decimal, getcontext
%o A369508 getcontext().prec = 100
%o A369508 def f(k):
%o A369508     if k == 1:
%o A369508         return prime(k) * Decimal(-0.5)
%o A369508     return f(k-1) + prime(k) * Decimal(-0.5) ** k
%o A369508 (PARI) suminf(k=1, prime(k)/(-2)^k) \\ _Michel Marcus_, Jan 25 2024
%Y A369508 Cf. A098990.
%K A369508 nonn,cons
%O A369508 0,1
%A A369508 _Pierluigi Failla_, Jan 25 2024