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A262645 Minimal nested palindromic base-6 primes with seed 0; see Comments.

%I A262645 #10 Oct 26 2015 22:24:30
%S A262645 0,101,5110115,13511011531,1135110115311,111351101153111,
%T A262645 152111351101153111251,5215211135110115311125125,
%U A262645 1025215211135110115311125125201,1431025215211135110115311125125201341,1111431025215211135110115311125125201341111
%N A262645 Minimal nested palindromic base-6 primes with seed 0; see Comments.
%C A262645 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 A262645 Clark Kimberling, <a href="/A262645/b262645.txt">Table of n, a(n) for n = 1..300</a>
%e A262645 a(3) = 5110115 is the least base-6 prime having a(2) = 101 in its middle.
%e A262645 Triangular format:
%e A262645          0
%e A262645         101
%e A262645       5110115
%e A262645     13511011531
%e A262645    1135110115311
%e A262645   111351101153111
%t A262645 s = {0}; base = 6; z = 20; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#, base]], base]] &];
%t A262645 AppendTo[s, FromDigits[IntegerDigits[tmp, base]]], {z}]; s  (* A262645 *)
%t A262645 Map[FromDigits[ToString[#], base] &, s]  (* A262646 *)
%t A262645 (* _Peter J. C. Moses_, Sep 01 2015 *)
%Y A262645 Cf. A261881 (base 10), A262646, A262627.
%K A262645 nonn,base
%O A262645 1,2
%A A262645 _Clark Kimberling_, Oct 24 2015