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 A262498 #10 Oct 02 2015 13:07:05
%S A262498 1111111,14111111141,131411111114131,91314111111141319,
%T A262498 389131411111114131983,7238913141111111413198327,
%U A262498 16723891314111111141319832761,381672389131411111114131983276183,1638167238913141111111413198327618361,1191638167238913141111111413198327618361911
%N A262498 Minimal nested palindromic primes with seed 1111111.
%C A262498 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 having a(n-1) in the middle. Then (a(n)) is the sequence of minimal nested palindromic primes with seed s.
%H A262498 Clark Kimberling, <a href="/A262498/b262498.txt">Table of n, a(n) for n = 1..200</a>
%e A262498 As a triangle:
%e A262498 1111111
%e A262498 14111111141
%e A262498 131411111114131
%e A262498 91314111111141319
%e A262498 389131411111114131983
%e A262498 7238913141111111413198327
%e A262498 16723891314111111141319832761
%e A262498 381672389131411111114131983276183
%t A262498 s0 = "1111111"; s = {ToExpression[s0]};Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s], 10, Max[StringLength[s0],Length[IntegerDigits[Last[s]]]]], Reverse[#]]&[IntegerDigits[#]]]] &]; AppendTo[s, tmp], {10}]; s0 <> ", " <> StringTake[ToString[Rest[s]], {2, -2}]
%t A262498 (* _Peter J. C. Moses_, Sep 23 2015 *)
%Y A262498 Cf. A261881.
%K A262498 nonn,base,easy
%O A262498 1,1
%A A262498 _Clark Kimberling_, Sep 24 2015