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 A261824 #8 Sep 29 2015 12:50:23
%S A261824 7,373,93739,129373921,3212937392123,34321293739212343,
%T A261824 353432129373921234353,1335343212937392123435331,
%U A261824 1171335343212937392123435331711,1051171335343212937392123435331711501,74105117133534321293739212343533171150147
%N A261824 Minimal nested palindromic primes with seed 7.
%C A261824 Let s be a palindrome and put a(1) = s. Let a(2) be the least palindromic prime having s in the middle; for n > 2, let a(n) be the least palindromic prime have a(n-1) in the middle. Then (a(n)) is the sequence of minimal nested palindromic primes with seed s.
%H A261824 Clark Kimberling, <a href="/A261824/b261824.txt">Table of n, a(n) for n = 1..200</a>
%e A261824 As a triangle:
%e A261824 ........7
%e A261824 .......373
%e A261824 ......93739
%e A261824 ....129373921
%e A261824 ..3212937392123
%e A261824 34321293739212343
%t A261824 s = {7}; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#]]]] &]; AppendTo[s, tmp], {15}]; s
%t A261824 (* _Peter J. C. Moses_, Sep 01 2015 *)
%Y A261824 Cf. A261881 (seed 0, with guide to related sequences).
%K A261824 nonn,easy,base
%O A261824 1,1
%A A261824 _Clark Kimberling_, Sep 23 2015