This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A139395 #8 Dec 20 2024 17:34:52
%S A139395 5,6,7,6,7,0,3,1,9,8,4,4,5,1,9,7,2,0,8,4,0,6,9,8,2,4,2,2,9,4,2,3,2,6,
%T A139395 7,2,5,5,8,1,1,4,8,1,3,7,3,4,6,7,3,7,8,6,3,8,3,4,2,4,9,4,7,0,5,4,8,5,
%U A139395 8,5,1,8,7,8,5,8,7,8,4,5,9,7,3,8,2,4,3,4,1,1,9,8,1,2,1,4,3,8,3,7
%N A139395 Decimal expansion of the sum 1/p(1) + 1/(p(2)*p(3)) + 1/(p(4)*p(5)*p(6)) + ..., where p(n) is the n-th prime.
%C A139395 Absolute difference between this number and A139396 is about 0.002.
%e A139395 0.56767031984451972084069824229423267255811481373467378638342..
%p A139395 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,105); od; print(a); end: P(100);
%t A139395 With[{nn=100},RealDigits[Total[1/Times@@@TakeList[Prime[Range[(nn(nn+1))/2]],Range[nn]]],10,120][[1]]] (* _Harvey P. Dale_, Dec 20 2024 *)
%Y A139395 Cf. A139396.
%K A139395 nonn,cons,easy
%O A139395 0,1
%A A139395 _Paolo P. Lava_ and _Giorgio Balzarotti_, Apr 18 2008