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%I #7 Nov 21 2013 12:47:57
%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..
%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); }
%K nonn
%O 1,1
%A _Cino Hilliard_, Feb 03 2003
%E Definition clarified and example provided by Harvey P. Dale, Mar 16 2011.
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