cp's OEIS Frontend

A139396 Decimal expansion of the alternating sum 1/p(1) + 1/(p(2)*p(3)) - 1/(p(4)*p(5)*p(6)) + 1/(p(7)*p(8)*p(9)*p(10)) - ..., where p(n) is the n-th prime.

%I A139396 #13 Feb 27 2014 03:38:26
%S A139396 5,6,5,6,7,2,2,9,6,8,0,3,0,6,1,8,9,7,7,0,3,8,4,2,4,8,6,9,7,5,1,6,2,7,
%T A139396 6,3,2,5,7,2,0,8,6,1,0,7,2,2,8,0,3,2,2,0,6,1,4,4,7,3,9,8,5,8,5,5,7,8,
%U A139396 8,4,9,4,5,8,3,9,0,5,3,1,9,5,9,2,6,1,0,3,8,0,1,3,1,3,8,5,7,0,8,4
%N A139396 Decimal expansion of the alternating sum 1/p(1) + 1/(p(2)*p(3)) - 1/(p(4)*p(5)*p(6)) + 1/(p(7)*p(8)*p(9)*p(10)) - ..., where p(n) is the n-th prime.
%C A139396 Absolute difference between this number and A139395 is about 0.002.
%e A139396 0.565672296803061897703842486975162763257208610722803220614...
%p A139396 P:=proc(n) local a,b,i,j,k; a:=0.5; k:=1; for i from 2 by 1 to n do b:=1; for j from k by 1 to k+i-1 do b:=b*1/ithprime(j+1); od; k:=j; a:=evalf(a+b*(-1)^i,105); od; print(a); end: P(100);
%Y A139396 Cf. A139395.
%K A139396 nonn,easy,cons
%O A139396 0,1
%A A139396 _Paolo P. Lava_ and _Giorgio Balzarotti_, Apr 18 2008
%E A139396 Definition corrected by _Bruno Berselli_, Feb 27 2014