This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A109945 #12 Nov 07 2017 18:29:39
%S A109945 3,5,11,29,41,71,137,281,461,599,641,827,881,1091,1301,1607,2129,2267,
%T A109945 2381,2687,3527,3557,3581,4127,4229,4337,4547,5009,5741,6131,6791,
%U A109945 6959,7211,7487,7547,8009,8597,8861,9041,9281,10007,10037,10427,10889,11117
%N A109945 Primes p such that [p,p+2] is a pair of twin primes and (p*(p+2)-1)/2 is prime.
%H A109945 Hugo Pfoertner, <a href="/A109945/b109945.txt">Table of n, a(n) for n = 1..10000</a>
%e A109945 3 is in the sequence because [3,5] is a pair of twin primes and (3*5 - 1)/2=7 is prime.
%t A109945 lst={}; d=2; Do[p1=Prime[n]; p2=Prime[n+1]; If[p2-p1==2&&PrimeQ[(p1*p2-1)/2], AppendTo[lst, p1]], {n, 10^3}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Aug 08 2008 *)
%Y A109945 Cf. A086870 [corresponding primes], A093706 [primes p such that (p*nextprime(p)-1)/2 is prime], A061351 [number separating twin pair is squarefree].
%K A109945 nonn
%O A109945 1,1
%A A109945 _Hugo Pfoertner_, Jul 09 2005