OFFSET
1,1
COMMENTS
Lesser of lonely twin primes.
Old Name was: Let P1,P2,..,P6 be any 6 consecutive primes. The sequence consists of those values of P3 for which P2-P1>2, P4-P3=2 and P6-P5>2.
LINKS
Sebastian Petzelberger, Table of n, a(n) for n = 1..10000
Hugo Pfoertner, FORTRAN program: Consecutive pairs of twin primes.
Randall Rathbun, A study of n-twin_prime clusters among prime numbers, Posting to Number Theory List, Nov 19 1998.
EXAMPLE
The first lonely twin primes (A069453) are 29,31 (23 and 37 are non-twin), 41,43 (37 and 47 are non-twin), 59,61 (53 and 67 are non-twin). Of these, the lesser twins are 29,41,59, so this is how the sequence begins.
23, 27, 29, 31, 37, 41: 27-23>2, 31-29=2, 41-37>2; so 29 is in the sequence.
From Hartmut F. W. Hoft, Apr 05 2016: (Start)
The example should read: 19, 23, 29, 31, 37, 41: 23-19>2, 31-29=2, 41-37>2; so 29 is in the sequence.
a(n)=A069453(2n-1), n>=1.
(End)
MATHEMATICA
PrimeNext[n_]:=Module[{k}, k=n+1; While[ !PrimeQ[k], k++ ]; k]; PrimePrev[n_]:=Module[{k}, k=n-1; While[ !PrimeQ[k], k-- ]; k]; lst={}; Do[p=Prime[n]; If[ !PrimeQ[p-2]&&!PrimeQ[p+4]&&PrimeQ[p+2]&&!PrimeQ[PrimePrev[p]-2]&&!PrimeQ[PrimeNext[p+2]+2], AppendTo[lst, p]], {n, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 22 2009 *)
(* starting at n=3 would eliminate the first two primality tests, Hartmut F. W. Hoft, Apr 09 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Randall L Rathbun, Nov 30 1998
EXTENSIONS
Edited by Hugo Pfoertner, Oct 15 2003
STATUS
approved