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A262637 Minimal nested palindromic base-4 primes with seed 2; see Comments.

%I A262637 #8 Oct 26 2015 22:23:35
%S A262637 2,323,3332333,333323333,33333233333,103333323333301,
%T A262637 1210333332333330121,100212103333323333301212001,
%U A262637 3310021210333332333330121200133,3303310021210333332333330121200133033,11330331002121033333233333012120013303311
%N A262637 Minimal nested palindromic base-4 primes with seed 2; see Comments.
%C A262637 Using only base-4 digits 0,1,2,3, 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-4 primes with seed s.
%H A262637 Clark Kimberling, <a href="/A262637/b262637.txt">Table of n, a(n) for n = 1..300</a>
%e A262637 a(3) = 3332333 is the least base-4 prime having a(2) = 323 in its middle.
%e A262637 Triangular format:
%e A262637          2
%e A262637         323
%e A262637       3332333
%e A262637      333323333
%e A262637     33333233333
%e A262637   103333323333301
%e A262637 1210333332333330121
%t A262637 s = {2}; base = 4; z = 20; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#, base]], base]] &];
%t A262637 AppendTo[s, FromDigits[IntegerDigits[tmp, base]]], {z}]; s  (* A262637 *)
%t A262637 Map[FromDigits[ToString[#], base] &, s]  (* A262638 *)
%t A262637 (* _Peter J. C. Moses_, Sep 01 2015 *)
%Y A262637 Cf. A261881 (base 10), A262638, A262627.
%K A262637 nonn,easy,base
%O A262637 1,1
%A A262637 _Clark Kimberling_, Oct 24 2015