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 A261823 #8 Sep 29 2015 12:30:58
%S A261823 6,10601,3106013,19310601391,3193106013913,30319310601391303,
%T A261823 3303193106013913033,333031931060139130333,33330319310601391303333,
%U A261823 303333031931060139130333303,1130333303193106013913033330311,19113033330319310601391303333031191
%N A261823 Minimal nested palindromic primes with seed 6.
%C A261823 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 A261823 Clark Kimberling, <a href="/A261823/b261823.txt">Table of n, a(n) for n = 1..200</a>
%e A261823 As a triangle:
%e A261823 ........6
%e A261823 ......10601
%e A261823 .....3106013
%e A261823 ...19310601391
%e A261823 ..3193106013913
%e A261823 30319310601391303
%t A261823 s = {6}; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#]]]] &]; AppendTo[s, tmp], {15}]; s
%t A261823 (* _Peter J. C. Moses_, Sep 01 2015 *)
%Y A261823 Cf. A261881 (seed 0, with guide to related sequences).
%K A261823 nonn,easy,base
%O A261823 1,1
%A A261823 _Clark Kimberling_, Sep 23 2015