%I #3 Oct 01 2013 17:57:43
%S 3,5,7,11,13,17,29,41,43,61,109,149,179,191,269,313,347,431,461,463,
%T 601,617,643,659,829,859,1031,1033,1051,1231,1279,1321,1619,1621,1879,
%U 1931,1949,1999,2029,2309,2311,2341,2383,2711,2789,2791,2801,3253,3299,3329
%N Twin prime indices of primes forming a twin prime member.
%C It is interesting that these primes occur rather frequently early on but gradually diminish as the iterations increase. Some ratios of count of twin primes p and the occurrence of prime(p) also a twin prime is as follows. Index< Ratio 1000 .74 10000 .48 100000 .39 1000000 .35 Looks like it is approaching a limit.
%e The 29th prime,109,is also a twin prime paired with the prime 107.
%o (PARI) twips(n) = { c1=0; c2=0; forprime(x=3,n, if(isprime(x+2),c1++); x1=prime(x); if(isprime(x-2) || isprime(x+2), if(isprime(x1-2) || isprime(x1+2), print1(x","); c2++; ) ) ); print(); print(c2/c1+.0) }
%K easy,nonn
%O 3,1
%A _Cino Hilliard_, Oct 21 2003