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%I #19 Nov 07 2015 03:22:51
%S 7,17,71,449,881,2591,9521,39761,106721,179999,206081,342791,388961,
%T 596231,847601,1292831,2268449,2571911,2836961,3612671,6223391,
%U 6329681,6415361,8520191,8946449,9409121,10342151,12550049,16485281,18800711
%N Primes equal to a product of twin primes minus 1 divided by 2.
%C From _Jason Kimberley_, Oct 22 2015 (Start)
%C Prime elements of A120876.
%C For each p in this list, A001221(2p) = A001222(2p) = A001221(2p+1) = A001222(2p+1) = 2.
%C 2*a(n) is a subsequence of A103533. They first differ when 313619 is not in this sequence, but 2*313619 = 627238 = A103533(12).
%C (End)
%H Jason Kimberley, <a href="/A086870/b086870.txt">Table of n, a(n) for n = 1..10000</a>
%F Primes of the form (t1*t2-1)/2, where t1, t2 are twin primes.
%e t1 = 71,t2 = 73, (71*73-1)/2 = 5182/2 = 2591 = prime.
%t Select[(Times[#, # + 2] - 1)/2 &@ Select[Prime@ Range@ 1000, PrimeQ[# + 2] &], PrimeQ] (* _Michael De Vlieger_, Nov 06 2015 *)
%o (PARI) for(n=1, 1e3, if(prime(n+1)-prime(n)==2 && isprime(k=(prime(n)*prime(n+1)-1)/2), print1(k", "))) \\ _Altug Alkan_, Nov 06 2015
%Y Cf. A103533, A120876.
%K easy,nonn
%O 1,1
%A _Cino Hilliard_, Aug 20 2003