%I #16 Jul 05 2024 05:08:42

%S 3,15,75,525,5775,75075,1276275,24249225,703227525,21800053275,

%T 893802184275,38433493923825,2267576141505675,138322144631846175,

%U 9820872268861078425,716923675626858725025,72409291238312731227525

%N Twin-primorial numbers: running products of twin primes.

%C The sum of the reciprocals converges to 0.4154254016622336549103692152614908366885449298862362851444631680740051...

%H Amiram Eldar, <a href="/A079164/b079164.txt">Table of n, a(n) for n = 1..309</a>

%e The first two twin primes are 3 and 5, so the first term is 3 and the second term is 15. The next two twin primes are 5 and 7, so the third term is 5*15=75 and the fourth term is 75*7=525

%t Rest[FoldList[Times,1,Flatten[Select[Partition[Prime[Range[30]], 2,1], Last[#]-First[#]==2&]]]] (* _Harvey P. Dale_, Mar 16 2011 *)

%o (PARI) twprfact(n) = {sr=0; tp = vector(10000); k=1; forprime(j = 3,n, if(nextprime(j+1)-j == 2, tp[k] = j; tp[k+1] = j+2; k+=2; ); ); for(j=1,k-1, y=1; for(i = 1,j, y*=tp[i]; ); print1(y", "); sr+=1.0/y; ); print(); print(sr); }

%Y Partial products of A077800.

%K nonn

%O 1,1

%A _Cino Hilliard_, Feb 03 2003

%E Definition clarified and example provided by _Harvey P. Dale_, Mar 16 2011