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A262635 Minimal nested base-4 palindromic primes with seed 1.

%I A262635 #9 Oct 23 2015 13:42:06
%S A262635 1,12121,111212111,31112121113,133111212111331,123133111212111331321,
%T A262635 303123133111212111331321303,3030312313311121211133132130303,
%U A262635 30303031231331112121113313213030303,3303030312313311121211133132130303033,11330303031231331112121113313213030303311
%N A262635 Minimal nested base-4 palindromic primes with seed 1.
%C A262635 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 base-4 palindromic primes with seed s.
%H A262635 Clark Kimberling, <a href="/A262635/b262635.txt">Table of n, a(n) for n = 1..300</a>
%e A262635 a(3) = 111212111 is the least base-4 prime having a(2) = 12121 in its middle. Triangular format:
%e A262635           1
%e A262635         12121
%e A262635       111212111
%e A262635      31112121113
%e A262635    133111212111331
%e A262635 123133111212111331321
%t A262635 s = {1}; base = 4; z = 20; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#, base]], base]] &];
%t A262635 AppendTo[s, FromDigits[IntegerDigits[tmp, base]]], {z}]; s  (* A262635 *)
%t A262635 Map[FromDigits[ToString[#], base] &, s]  (* A262636 *)
%t A262635 (* _Peter J. C. Moses_, Sep 01 2015 *)
%Y A262635 Cf. A261881 (base 10), A262636, A262627. Subsequence of A117699.
%K A262635 nonn,base
%O A262635 1,2
%A A262635 _Clark Kimberling_, Oct 02 2015