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 A035790 #40 Apr 03 2023 10:36:09
%S A035790 101,137,419,1019,1049,1481,1871,1931,2081,2111,2969,3251,3461,4259,
%T A035790 5009,5651,5867,6689,6947,7331,7547,8219,8969,10007,11057,11159,11699,
%U A035790 12239,13001,13709,13997,14561,15641,15731,16061,16631,17579,17909
%N A035790 Start of a string of exactly 2 consecutive (but disjoint) pairs of twin primes.
%C A035790 Let P1,P2,..,P8 be any 8 consecutive primes. The sequence consists of those values of P3 for which P2-P1 > 2, P4-P3 = 2, P6-P5= 2 and P8-P7 > 2.
%D A035790 Posting to Number Theory List (NMBRTHRY(AT)LISTSERV.NODAK.EDU), Nov. 19 1998.
%H A035790 Sebastian Petzelberger, <a href="/A035790/b035790.txt">Table of n, a(n) for n = 1..10000</a>
%H A035790 G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/cpage/18800.html">10000...01521 (100-digits)</a>
%H A035790 Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a035789.txt">FORTRAN program: Consecutive pairs of twin primes</a>.
%F A035790 a(10)=2111, a(10^2)=77261, a(10^3)=1603697, a(10^4)=27397631, a(10^5)=435140477, a(10^6)=6391490657. - _M. F. Hasler_, May 04 2015
%e A035790 89, 97, 101, 103, 107, 109, 113, 127: 97-89 > 2, 103-101 = 2, 109-107 = 2, 127-113 > 2.
%t A035790 Select[Prime@ Range@ 2100, And[NextPrime[#, -1] - NextPrime[#, -2] > 2, NextPrime@ # - # == 2, NextPrime[#, 3] - NextPrime[#, 2] == 2, NextPrime[#, 5] - NextPrime[#, 4] > 2] &] (* _Michael De Vlieger_, Apr 25 2015 *)
%o A035790 (PARI) a(n)={L=vector(7);forprime(p=o=1,,L=concat(L[2..7],-o+o=p); L[3]==2&&L[5]==2&&L[1]>2&&L[2]>2&&L[4]>2&&L[6]>2&&L[7]>2&&!n--&&return(p-sum(i=3,7,L[i])))} \\ _M. F. Hasler_, May 04 2015
%Y A035790 Cf. A035789, A035791, A035792, A035793, A035794, A035795, A087641.
%K A035790 nonn,easy
%O A035790 1,1
%A A035790 _Randall L Rathbun_, Nov 30 1998
%E A035790 Edited by _Hugo Pfoertner_, Oct 15 2003
%E A035790 Offset corrected by _Arkadiusz Wesolowski_, May 06 2012
%E A035790 Double-checked up to a(10^4)=27397631 by _M. F. Hasler_, May 04 2015