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%I #14 Apr 10 2019 14:33:32
%S 15,55,341,1003,3161,7339,16343,25063,55247,62809,105901,127991,
%T 190277,220223,236597,325291,358261,463487,512263,641593,812327,
%U 1213843,1293431,1502399,1944893,2351677,2633803,2806733,3050519,3250847
%N Product of twin-prime-indexed primes and their lower bound twin prime.
%H Harvey P. Dale, <a href="/A080698/b080698.txt">Table of n, a(n) for n = 1..1000</a>
%F Let prime(i) = i-th prime, let twin(n) = (P, Q) be n-th pair of twin primes; sequence gives prime(P)*P.
%e The 3rd pair of twin primes is twin(3) = (11,13), prime(11) = 31. a(3) = 31*11 = 341.
%t # Prime[#]&/@Select[Partition[Prime[Range[200]],2,1],#[[2]]-#[[1]]==2&][[All,1]] (* _Harvey P. Dale_, Apr 10 2019 *)
%o (PARI) twipxpindex(n) = {sr=0; pr=1; for(x=1,n, p1=prime(x); p2=prime(x+1); if((p2-p1)==2, pr=p1*prime(prime(x)); sr+=1.0/pr; print1(pr" ")); ); print(); print(sr) }
%Y Cf. A057470.
%K easy,nonn
%O 1,1
%A _Cino Hilliard_, Mar 04 2003