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Decimal expansion of the sum_{n>0} of A000040(n)/exp(n), where A000040(k) gives the k-th prime number and exp(k) is the natural exponential of k.
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%I #6 Dec 18 2013 16:39:18

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

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

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

%N Decimal expansion of the sum_{n>0} of A000040(n)/exp(n), where A000040(k) gives the k-th prime number and exp(k) is the natural exponential of k.

%C Relates the growth of the n-th-prime function A000040(n) to the growth of the natural exponential exp(n)=e^n where e is Euler's number (A001113).

%e 1.65217939256105495588822076145765122466474170334941178449725933662968594748369163520525391269497983139285...

%p f:=x->sum(ithprime(n)/exp(n),n=1..x); evalf[110](f(1500)); evalf[110](f(4000));

%t RealDigits[Total[Table[Prime[k]/Exp[k],{k,2000}]],10,110][[1]] (* _Harvey P. Dale_, Dec 18 2013 *)

%Y Cf. A000040, A001113.

%K cons,nonn

%O 1,2

%A Joseph Biberstine (jrbibers(AT)indiana.edu), Nov 03 2004