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A262643 Minimal nested palindromic base-5 primes with seed 3; see Comments.

%I A262643 #10 Oct 26 2015 22:24:14
%S A262643 3,131,31313,1313131,413131314,2341313131432,40234131313143204,
%T A262643 144023413131314320441,2314402341313131432044132,
%U A262643 2202314402341313131432044132022,14220231440234131313143204413202241,20114220231440234131313143204413202241102
%N A262643 Minimal nested palindromic base-5 primes with seed 3; see Comments.
%C A262643 Using only base-5 digits 0,1,2,3,4, 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-5 primes with seed s.
%H A262643 Clark Kimberling, <a href="/A262643/b262643.txt">Table of n, a(n) for n = 1..300</a>
%e A262643 a(3) = 31313 is the least base-5 prime having a(2) = 131 in its middle.
%e A262643 Triangular format:
%e A262643       3
%e A262643      131
%e A262643     31313
%e A262643    1313131
%e A262643   413131314
%e A262643 2341313131432
%t A262643 s = {3}; base = 5; z = 20; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#, base]], base]] &];
%t A262643 AppendTo[s, FromDigits[IntegerDigits[tmp, base]]], {z}]; s  (* A262643 *)
%t A262643 Map[FromDigits[ToString[#], base] &, s]  (* A262644 *)
%t A262643 (* _Peter J. C. Moses_, Sep 01 2015 *)
%Y A262643 Cf. A261881 (base 10), A262644, A262627.
%K A262643 nonn,base
%O A262643 1,1
%A A262643 _Clark Kimberling_, Oct 24 2015