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 A334885 #10 May 26 2020 22:22:16
%S A334885 3,2,13681,467,127787377,200603842261
%N A334885 Let q = p | p' be the digit concatenation of a prime p with its prime successor. If the result is a prime repeat the construction setting p = q. a(n) is the smallest prime for which this can be repeated exactly n times.
%C A334885 a(6) > 10^13.
%H A334885 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_029.htm">Puzzle 29. P_i = P_(i-1) & nxtprm(P_(i-1)), P_i = prime for i => 1</a>, The Prime Puzzles and Problems Connection.
%e A334885 Let "|" denote concatenation.
%e A334885 3 | 5 = 35, which is not prime, so a(0) = 3.
%e A334885 2 | 3 = 23 (prime), 23 | 29 = 2329 (composite), so a(1) = 2.
%e A334885 13681 | 13687 (prime), 1368113687 | 1368113699 (prime), 13681136871368113699 | 13681136871368113711 (composite), so a(2) = 13681.
%t A334885 a[n_] := Block[{pp=1, p, q, c=-1}, While[ c!=n, c=0; p = pp = NextPrime@ pp; While[ PrimeQ[ q = FromDigits[ Join @@ IntegerDigits@{p, NextPrime@ p}]], c++; p = q]]; pp]; a /@ Range[0, 3]
%Y A334885 Cf. A030459, A034593, A036339, A036340, A036341.
%K A334885 nonn,base,more
%O A334885 0,1
%A A334885 _Giovanni Resta_, May 14 2020