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%I A035789 #42 Jun 24 2022 04:41:33
%S A035789 29,41,59,71,227,239,269,281,311,347,461,521,569,599,617,641,659,857,
%T A035789 881,1091,1151,1229,1277,1289,1301,1319,1427,1451,1607,1619,1667,1697,
%U A035789 1721,1787,1997,2027,2141,2237,2267,2309,2339,2381,2549,2591,2657,2687
%N A035789 Start of a string of exactly 1 consecutive (but disjoint) pair of twin primes.
%C A035789 Lesser of lonely twin primes.
%C A035789 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.
%H A035789 Sebastian Petzelberger, <a href="/A035789/b035789.txt">Table of n, a(n) for n = 1..10000</a>
%H A035789 Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a035789.txt">FORTRAN program: Consecutive pairs of twin primes</a>.
%H A035789 Randall Rathbun, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;6a849ab3.9811">A study of n-twin_prime clusters among prime numbers</a>, Posting to Number Theory List, Nov 19 1998.
%e A035789 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.
%e A035789 23, 27, 29, 31, 37, 41: 27-23>2, 31-29=2, 41-37>2; so 29 is in the sequence.
%e A035789 From _Hartmut F. W. Hoft_, Apr 05 2016: (Start)
%e A035789 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.
%e A035789 a(n)=A069453(2n-1), n>=1.
%e A035789 (End)
%t A035789 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 *)
%t A035789 (* starting at n=3 would eliminate the first two primality tests, _Hartmut F. W. Hoft_, Apr 09 2016 *)
%Y A035789 Cf. A035790, A035791, A035792, A035793, A035794, A035795, A087641.
%Y A035789 Cf. A069453, A069455.
%K A035789 nonn,easy
%O A035789 1,1
%A A035789 _Randall L Rathbun_, Nov 30 1998
%E A035789 Edited by _Hugo Pfoertner_, Oct 15 2003

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