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%I A262499 #10 Oct 02 2015 13:09:00
%S A262499 111111111,1311111111131,31131111111113113,3311311111111131133,
%T A262499 333113111111111311333,3033311311111111131133303,
%U A262499 1323033311311111111131133303231,313230333113111111111311333032313,9531323033311311111111131133303231359
%N A262499 Minimal nested palindromic primes with seed 111111111.
%C A262499 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 A262499 Clark Kimberling, <a href="/A262499/b262499.txt">Table of n, a(n) for n = 1..200</a>
%e A262499 As a triangle:
%e A262499               111111111
%e A262499             1311111111131
%e A262499           31131111111113113
%e A262499          3311311111111131133
%e A262499         333113111111111311333
%e A262499       3033311311111111131133303
%e A262499    1323033311311111111131133303231
%e A262499   313230333113111111111311333032313
%t A262499 s0 = "111111111"; 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 A262499 (* _Peter J. C. Moses_, Sep 23 2015 *)
%Y A262499 Cf. A261881.
%K A262499 nonn,base,easy
%O A262499 1,1
%A A262499 _Clark Kimberling_, Sep 24 2015

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