login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A035789 Start of a string of exactly 1 consecutive (but disjoint) pair of twin primes. 17

%I #42 Jun 24 2022 04:41:33

%S 29,41,59,71,227,239,269,281,311,347,461,521,569,599,617,641,659,857,

%T 881,1091,1151,1229,1277,1289,1301,1319,1427,1451,1607,1619,1667,1697,

%U 1721,1787,1997,2027,2141,2237,2267,2309,2339,2381,2549,2591,2657,2687

%N Start of a string of exactly 1 consecutive (but disjoint) pair of twin primes.

%C Lesser of lonely twin primes.

%C 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 Sebastian Petzelberger, <a href="/A035789/b035789.txt">Table of n, a(n) for n = 1..10000</a>

%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a035789.txt">FORTRAN program: Consecutive pairs of twin primes</a>.

%H 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 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 23, 27, 29, 31, 37, 41: 27-23>2, 31-29=2, 41-37>2; so 29 is in the sequence.

%e From _Hartmut F. W. Hoft_, Apr 05 2016: (Start)

%e 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 a(n)=A069453(2n-1), n>=1.

%e (End)

%t 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 (* starting at n=3 would eliminate the first two primality tests, _Hartmut F. W. Hoft_, Apr 09 2016 *)

%Y Cf. A035790, A035791, A035792, A035793, A035794, A035795, A087641.

%Y Cf. A069453, A069455.

%K nonn,easy

%O 1,1

%A _Randall L Rathbun_, Nov 30 1998

%E Edited by _Hugo Pfoertner_, Oct 15 2003

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)