A069453 Lonely twin primes.

29, 31, 41, 43, 59, 61, 71, 73, 227, 229, 239, 241, 269, 271, 281, 283, 311, 313, 347, 349, 461, 463, 521, 523, 569, 571, 599, 601, 617, 619, 641, 643, 659, 661, 857, 859, 881, 883, 1091, 1093, 1151, 1153, 1229, 1231, 1277, 1279, 1289

Offset: 1

Author

Neil Fernandez, Mar 22 2002

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A001097, A035789, A069455.

Programs

Mathematica

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]
Flatten[a069453[1000]] (* isolated prime pairs less than 1000 *)
(* Hartmut F. W. Hoft, Apr 09 2016 *)

Formula

a(2n-1) = A035789(n) and a(2n) = A069455(n), for n>=1. - Hartmut F. W. Hoft, Apr 09 2016