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A262651 Minimal nested palindromic base-6 primes with seed 3; see Comments.

%I A262651 #6 Oct 31 2015 15:03:02
%S A262651 3,11311,121131121,5312113112135,14531211311213541,
%T A262651 1145312113112135411,51114531211311213541115,
%U A262651 5511145312113112135411155,50551114531211311213541115505,115055111453121131121354111550511,51150551114531211311213541115505115
%N A262651 Minimal nested palindromic base-6 primes with seed 3; see Comments.
%C A262651 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 A262651 Clark Kimberling, <a href="/A262651/b262651.txt">Table of n, a(n) for n = 1..300</a>
%e A262651 a(3) = 121131121 is the least base-6 prime having a(2) = 11311 in its middle. Triangular format:
%e A262651         3
%e A262651       11311
%e A262651     121131121
%e A262651   5312113112135
%e A262651 14531211311213541
%t A262651 s = {3}; base = 6; z = 20; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#, base]], base]] &];
%t A262651 AppendTo[s, FromDigits[IntegerDigits[tmp, base]]], {z}]; s  (* A262651 *)
%t A262651 Map[FromDigits[ToString[#], base] &, s]  (* A262652 *)
%t A262651 (* _Peter J. C. Moses_, Sep 01 2015 *)
%Y A262651 Cf. A261881 (base 10), A262652, A262627.
%K A262651 nonn,easy,base
%O A262651 1,1
%A A262651 _Clark Kimberling_, Oct 27 2015