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 A063502 #25 Mar 12 2022 22:43:06
%S A063502 1,3,11,137,5639,641129,152921807,65818751039,46091763604421
%N A063502 a(n+1) = p, where p is the a(n)-th twin prime (p,p+2), with a(0) = 1.
%C A063502 Instead of starting with a(0) = 1 for the first twin prime (3,5) other sequences can be formed for a(0) = 2, i.e. 2nd twin prime: 2, 5, 29, 641, 44381, 7212059, etc., a(0) = 4: 4, 17, 239, 12161, 1583927, etc., a(0) = 6: 6, 41, 1151, 93251, 16989317, etc., a(0) = 7: 7, 59 1931,176021, 35263691, etc., a(0) = 8: 8, 71, 2339,221201, 45749309 and so on.
%H A063502 Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/primes.html">Tables of values of pi(x) and of pi2(x)</a> [From _M. F. Hasler_, Mar 02 2009]
%F A063502 a(n+1) = A001359(a(n)); a(0)=1. [_M. F. Hasler_, Mar 02 2009]
%e A063502 a(3) = 137 because a(2) = 11 and the 11th twin prime is (137,139).
%t A063502 (* Computes up to a(6) only *) tp[n_] := (* = A001359 *) tp[n] = (p = NextPrime[tp[n-1]]; While[ !PrimeQ[p+2], p = NextPrime[p]]; p); tp[1] = 3; Do[tp[n], {n, 2, 10^6}]; a[n_] := a[n] = tp[a[n-1]]; a[0]=1; Table[ Print[ a[n]]; a[n], {n, 0, 6}] (* _Jean-François Alcover_, Dec 13 2011 *)
%Y A063502 Cf. A007097.
%K A063502 hard,more,nice,nonn
%O A063502 0,2
%A A063502 _Lubomir Alexandrov_, Jul 30 2001
%E A063502 Edited by _Frank Ellermann_, Jan 25 2002
%E A063502 Offset and example corrected by _Farideh Firoozbakht_, Dec 07 2008
%E A063502 a(7) = 65818751039 from _Zak Seidov_ and _Farideh Firoozbakht_, Dec 13 2008
%E A063502 Computed a(8)=46091763604421 using data from T. Oliveira e Silva. - _M. F. Hasler_, Mar 02 2009