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

1,1

Links

Table of n, a(n) for n=1..47.

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A001097, A035789, A069455.

Sequence in context: A288879 A102906 A178456 * A104071 A288616 A273547

Adjacent sequences: A069450 A069451 A069452 * A069454 A069455 A069456

Keyword

nonn

Author

Neil Fernandez, Mar 22 2002

Status

approved