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%I #15 Nov 16 2020 03:39:20
%S 3,9,6,4,7,8,4,0,0,1,7,6,7,2,8,8,0,1,3,2,0,3,7,7,2,1,9,5,4,9,1,4,5,0,
%T 1,3,1,1,7,8,3,7,6,1,4,2,2,1,9,0,4,1,8,5,1,5,8,6,6,3,8,8,9,5,4,4,0,1,
%U 0,8,7,8,0,8,5,0,8,7,7,9,9,7,0,3,9,5,5,5,9,1,1,1,0,5,2,9,9,2,9,0,2,5,5,9,8
%N Decimal expansion of Sum_{n = 1 .. infinity } (-1)^(n+1)/ prime(n)^n.
%e 0.39647840017672880132037721... = 1/2^1 - 1/3^2 + 1/5^3 - 1/7^4 + ...
%p with(numtheory): Digits:=105:s:=sum( evalf(((-1)^(n+1))/ ithprime(n)^n),n=1..200):print(s):
%t digits = 105; NSum[(-1)^(n+1)/Prime[n//Round]^n, {n, 1, Infinity}, Method -> "AlternatingSigns", WorkingPrecision -> digits, NSumTerms -> digits] // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Feb 24 2014 *)
%Y Cf. A062457, A093358.
%K nonn,cons
%O 0,1
%A _Michel Lagneau_, Dec 03 2011