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%I #10 Apr 10 2016 10:17:23
%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(2n-1) = 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 non-twin) and 41,43 (37 and 47 are non-twin). 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
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