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A262639 Minimal nested palindromic base-4 primes with seed 3; see Comments.

%I A262639 #8 Oct 26 2015 22:24:00
%S A262639 3,131,11311,121131121,1212113112121,312121131121213,
%T A262639 101312121131121213101,11131013121211311212131013111,
%U A262639 31311131013121211311212131013111313,1011313111310131212113112121310131113131101,310113131113101312121131121213101311131311013
%N A262639 Minimal nested palindromic base-4 primes with seed 3; see Comments.
%C A262639 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 A262639 Clark Kimberling, <a href="/A262639/b262639.txt">Table of n, a(n) for n = 1..300</a>
%e A262639 a(3) = 11311 is the least base-4 prime having a(2) = 131 in its middle.
%e A262639 Triangular format:
%e A262639          3
%e A262639         131
%e A262639        11311
%e A262639      121131121
%e A262639    1212113112121
%e A262639   312121131121213
%t A262639 s = {3}; base = 4; z = 20; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#, base]], base]] &];
%t A262639 AppendTo[s, FromDigits[IntegerDigits[tmp, base]]], {z}]; s  (* A262639 *)
%t A262639 Map[FromDigits[ToString[#], base] &, s]  (* A262640 *)
%t A262639 (* _Peter J. C. Moses_, Sep 01 2015 *)
%Y A262639 Cf. A261881 (base 10), A262640, A262627.
%K A262639 nonn,easy,base
%O A262639 1,1
%A A262639 _Clark Kimberling_, Oct 24 2015