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A262633 Minimal nested base-4 palindromic primes with seed 0.

%I A262633 #9 Oct 23 2015 13:41:23
%S A262633 0,101,31013,3310133,1023310133201,3331023310133201333,
%T A262633 3223331023310133201333223,1133223331023310133201333223311,
%U A262633 100311332233310233101332013332233113001,10231003113322333102331013320133322331130013201
%N A262633 Minimal nested base-4 palindromic primes with seed 0.
%C A262633 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 A262633 Clark Kimberling, <a href="/A262633/b262633.txt">Table of n, a(n) for n = 1..300</a>
%e A262633 a(3) = 31013 is the least base-4 prime having a(2) = 101 in its middle. Triangular format:
%e A262633          0
%e A262633         101
%e A262633        31013
%e A262633       3310133
%e A262633    1023310133201
%e A262633 3331023310133201333,
%t A262633 s = {0}; base = 4; z = 20; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#, base]], base]] &];
%t A262633 AppendTo[s, FromDigits[IntegerDigits[tmp, base]]], {z}]; s  (* A262633 *)
%t A262633 Map[FromDigits[ToString[#], base] &, s]  (* A262634 *)
%t A262633 (* _Peter J. C. Moses_, Sep 01 2015 *)
%Y A262633 Cf. A261881 (base 10), A262634, A262627. Subsequence of A117699.
%K A262633 nonn,base
%O A262633 1,2
%A A262633 _Clark Kimberling_, Oct 02 2015