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 A261825 #8 Sep 29 2015 12:50:07
%S A261825 8,181,1218121,15121812151,111512181215111,3311151218121511133,
%T A261825 133111512181215111331,1113311151218121511133111,
%U A261825 1141113311151218121511133111411,73114111331115121812151113311141137,30273114111331115121812151113311141137203
%N A261825 Minimal nested palindromic primes with seed 8.
%C A261825 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 A261825 Clark Kimberling, <a href="/A261825/b261825.txt">Table of n, a(n) for n = 1..200</a>
%e A261825 As a triangle:
%e A261825 .........8
%e A261825 ........181
%e A261825 ......1218121
%e A261825 ....15121812151
%e A261825 ..111512181215111
%e A261825 3311151218121511133
%t A261825 s = {8}; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#]]]] &]; AppendTo[s, tmp], {15}]; s
%t A261825 (* _Peter J. C. Moses_, Sep 01 2015 *)
%Y A261825 Cf. A261881 (seed 0, with guide to related sequences).
%K A261825 nonn,easy,base
%O A261825 1,1
%A A261825 _Clark Kimberling_, Sep 23 2015