This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A089628 #15 Jun 25 2021 23:34:18
%S A089628 3,5,11,101,137,179,191,419,809,821,1019,1049,1481,1871,1931,2081,
%T A089628 2111,2969,3251,3359,3371,3461,4217,4229,4259,5009,5651,5867,6689,
%U A089628 6761,6779,6947,7331,7547,8219,8969,9419,9431,9437,10007,11057,11159,11699,12239
%N A089628 Smallest member of a pair of consecutive twin prime pairs that have no primes between them.
%C A089628 Run the PARI script savetwins(100000) or so to build the twinprime array of lower bounds before you run the main script.
%C A089628 Except for first term, same as A053778. - _David Wasserman_, Feb 22 2006
%H A089628 Harvey P. Dale, <a href="/A089628/b089628.txt">Table of n, a(n) for n = 3..1000</a>
%e A089628 Twin prime pairs 5,7 and 11,13 contain only the composite numbers 6,7,8,9,10 between them. So 5 is in the table. 11,13 and 17,19 have no primes between.
%e A089628 11 is in the table. 41,43 and 59,61 have primes 47 and 53 between then so 41 is not listed.
%t A089628 Join[{3},Select[Partition[Prime[Range[1500]],4,1],#[[4]]-#[[3]]==#[[2]]- #[[1]] == 2&][[All,1]]] (* _Harvey P. Dale_, Dec 15 2018 *)
%o A089628 (PARI) \save as twinpr.gp pbetweentw(n) = { forstep(x1=1,n,2, c=0; t1 = twin[x1]; t2 = twin[x1+2]; for(y=t1+3,t2-1, if(isprime(y),c++) ); if(c==0,print1(t1",")) ) } savetwins(n) = build a table of twin prime I want to upload a supporting file to store with the OEIS and add a link to it.lower bounds { twin = vector(n); c=1; forprime(x=3,n, if(isprime(x+2), twin[c]=x; c++; ) ) }
%K A089628 easy,nonn
%O A089628 3,1
%A A089628 _Cino Hilliard_, Jan 01 2004