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A262647 Minimal nested palindromic base-6 primes with seed 1; see Comments.

%I A262647 #8 Oct 26 2015 22:24:45
%S A262647 1,111,1111111,14111111141,111411111114111,103111411111114111301,
%T A262647 5510311141111111411130155,10551031114111111141113015501,
%U A262647 501055103111411111114111301550105,102501055103111411111114111301550105201,5110250105510311141111111411130155010520115
%N A262647 Minimal nested palindromic base-6 primes with seed 1; see Comments.
%C A262647 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 A262647 Clark Kimberling, <a href="/A262647/b262647.txt">Table of n, a(n) for n = 1..300</a>
%e A262647 a(3) = 1111111 is the least base-6 prime having a(2) = 111 in its middle. Triangular format:
%e A262647           1
%e A262647          111
%e A262647        1111111
%e A262647      14111111141
%e A262647    111411111114111
%e A262647 103111411111114111301
%t A262647 s = {1}; base = 6; z = 20; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#, base]], base]] &];
%t A262647 AppendTo[s, FromDigits[IntegerDigits[tmp, base]]], {z}]; s  (* A262647 *)
%t A262647 Map[FromDigits[ToString[#], base] &, s]  (* A262648 *)
%t A262647 (* _Peter J. C. Moses_, Sep 01 2015 *)
%Y A262647 Cf. A261881 (base 10), A262648, A262627.
%K A262647 nonn,base
%O A262647 1,2
%A A262647 _Clark Kimberling_, Oct 25 2015