%I #24 Dec 02 2022 15:42:39

%S 6,30,42,462,6006,102102,1939938,44618574,1293938646,40112098026,

%T 1484147626962,60850052705442,2616552266334006,122977956517698282,

%U 6517831695438008946,7255699434544198638,442597665507196116918,29654043588982139833506,2105437094817731928178926,153696907921694430757061598

%N Denominator of Sum_{i=1..n} 1/(prime(i)*prime(i+1)).

%C a(371) has 1003 decimal digits. - _Michael De Vlieger_, Jan 27 2016

%H Michael De Vlieger, <a href="/A241190/b241190.txt">Table of n, a(n) for n = 1..370</a>

%e 1/6, 7/30, 11/42, 127/462, 1693/6006, 29243/102102, 561623/1939938, 13019431/44618574, 379503437/1293938646, 11809225121/40112098026, 438235268123/1484147626962, ...

%p g:= n-> add(1/(ithprime(i)*ithprime(i+1)),i=1..n);

%p t1:=[seq(g(n),n=1..20)];

%p t1a:=map(numer,t1); # A241189

%p t1b:=map(denom,t1); # A241190

%t Table[Denominator@ Sum[1/(Prime[i + 1] Prime@ i), {i, n}], {n, 20}] (* _Michael De Vlieger_, Jan 27 2016 *)

%o (PARI) a(n) = denominator(sum(k=1, n, 1/(prime(k)*prime(k+1)))); \\ _Michel Marcus_, Jan 27 2016

%Y Cf. A024451/A002110, A241189/A241190, A241191/A241192.

%K nonn,frac

%O 1,1

%A _N. J. A. Sloane_, Apr 25 2014, based on a suggestion from _Timothy Varghese_.