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A262653 Minimal nested palindromic base-6 primes with seed 4; see Comments.

%I A262653 #6 Oct 31 2015 15:03:18
%S A262653 4,141,11411,5114115,551141155,1455114115541,1111455114115541111,
%T A262653 55111145511411554111155,1021551111455114115541111551201,
%U A262653 12102155111145511411554111155120121,531210215511114551141155411115512012135,101531210215511114551141155411115512012135101
%N A262653 Minimal nested palindromic base-6 primes with seed 4; see Comments.
%C A262653 Using only base-6 digits 0,1,2,3,4,5, 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 base-6 primes with seed s.
%H A262653 Clark Kimberling, <a href="/A262653/b262653.txt">Table of n, a(n) for n = 1..300</a>
%e A262653 a(3) = 11411 is the least base-6 prime having a(2) = 141 in its middle. Triangular format:
%e A262653       4
%e A262653      141
%e A262653     11411
%e A262653    5114115
%e A262653   551141155
%e A262653 1455114115541
%t A262653 s = {4}; base = 6; z = 20; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#, base]], base]] &];
%t A262653 AppendTo[s, FromDigits[IntegerDigits[tmp, base]]], {z}]; s  (* A262653 *)
%t A262653 Map[FromDigits[ToString[#], base] &, s]  (* A262654 *)
%t A262653 (* _Peter J. C. Moses_, Sep 01 2015 *)
%Y A262653 Cf. A261881 (base 10), A262654, A262627.
%K A262653 nonn,easy,base
%O A262653 1,1
%A A262653 _Clark Kimberling_, Oct 27 2015