A080700 Product of upper bound twin-prime-indexed primes and their lower bound twin prime.
33, 85, 451, 1139, 3683, 7831, 16697, 26057, 56863, 64093, 109189, 130673, 194573, 223661, 239749, 328469, 363997, 468329, 519007, 647191, 815797, 1218871, 1301189, 1520839, 1959481, 2363057, 2648179, 2817839, 3068467, 3257437
Offset: 1
Examples
The 3rd pair of twin primes is twin(3) = (11,13), prime(13) = 41, a(3) = 41*11 = 451.
Programs
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Mathematica
Prime[Last[#]]First[#]&/@Select[Partition[Prime[Range[200]],2,1], Last[#]- First[#] ==2&] (* Harvey P. Dale, Apr 23 2011 *)
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PARI
twipxpindex3(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+1)); sr+=1.0/pr; print1(pr" ")); ); print(); print(sr) }
Formula
Let prime(i) = i-th prime, let twin(n) = (P, Q) be n-th pair of twin primes; sequence gives prime(Q)*P.