A201614 Decimal expansion of Sum_{n = 1 .. infinity } (-1)^(n+1)/ prime(n)^n.
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, 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, 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
Offset: 0
Examples
0.39647840017672880132037721... = 1/2^1 - 1/3^2 + 1/5^3 - 1/7^4 + ...
Programs
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Maple
with(numtheory): Digits:=105:s:=sum( evalf(((-1)^(n+1))/ ithprime(n)^n),n=1..200):print(s):
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Mathematica
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 *)