%I
%S 29,31,41,43,59,61,71,73,227,229,239,241,269,271,281,283,311,313,347,
%T 349,461,463,521,523,569,571,599,601,617,619,641,643,659,661,857,859,
%U 881,883,1091,1093,1151,1153,1229,1231,1277,1279,1289
%N Lonely twin primes.
%F a(2n1) = A035789(n) and a(2n) = A069455(n), for n>=1.  _Hartmut F. W. Hoft_, Apr 09 2016
%e The first twin primes that are not adjacent to twin primes other than their own twins are 29,31 (23 and 37 are nontwin) and 41,43 (37 and 47 are nontwin). So the sequence begins 29,31,41,43.
%t a069453[n_] := Module[{c6p={3, 5, 7, 11, 13, 17}, seq={}, i=6, last=17}, While[i<=n, If[c6p[[4]]c6p[[3]]==2 && c6p[[2]]c6p[[1]]>2 && c6p[[6]]c6p[[5]]>2, AppendTo[seq, {c6p[[3]], c6p[[4]]}]]; last=NextPrime[last]; c6p=Append[Drop[c6p, 1], last]; i++]; seq]
%t Flatten[a069453[1000]] (* isolated prime pairs less than 1000 *)
%t (* _Hartmut F. W. Hoft_, Apr 09 2016 *)
%Y Cf. A001097, A035789, A069455.
%K nonn
%O 1,1
%A _Neil Fernandez_, Mar 22 2002
