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 A241189 #14 Jul 09 2025 04:38:33
%S A241189 1,7,11,127,1693,29243,561623,13019431,379503437,11809225121,
%T A241189 438235268123,18007758091069,775817745542929,36524284093223105,
%U A241189 1938403609207158571,2160165866032831207,131893095784520401909,8844093116997411126541,628373208972323386101329,45900898298568589325230523
%N A241189 Numerator of Sum_{i=1..n} 1/(prime(i)*prime(i+1)).
%C A241189 a(371) has 1002 decimal digits. - _Michael De Vlieger_, Jan 27 2016
%H A241189 Michael De Vlieger, <a href="/A241189/b241189.txt">Table of n, a(n) for n = 1..370</a>
%e A241189 1/6, 7/30, 11/42, 127/462, 1693/6006, 29243/102102, 561623/1939938, 13019431/44618574, 379503437/1293938646, 11809225121/40112098026, 438235268123/1484147626962, ...
%p A241189 g:= n-> add(1/(ithprime(i)*ithprime(i+1)),i=1..n);
%p A241189 t1:=[seq(g(n),n=1..20)];
%p A241189 t1a:=map(numer,t1); # A241189
%p A241189 t1b:=map(denom,t1); # A241190
%t A241189 Table[Numerator@ Sum[1/(Prime[i + 1] Prime@ i), {i, n}], {n, 20}] (* _Michael De Vlieger_, Jan 27 2016 *)
%t A241189 Accumulate[1/#&/@(Times@@@Partition[Prime[Range[25]],2,1])]//Numerator (* _Harvey P. Dale_, Mar 14 2023 *)
%Y A241189 Cf. A024451/A002110, A241189/A241190, A241191/A241192.
%Y A241189 See also A061015/A061742, A115963/A115964.
%K A241189 nonn,frac
%O A241189 1,2
%A A241189 _N. J. A. Sloane_, Apr 25 2014, based on a suggestion from _Timothy Varghese_