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A262641 Minimal nested palindromic base-5 primes with seed 1; see Comments.

%I A262641 #10 Oct 25 2015 17:58:52
%S A262641 1,111,41114,1411141,20141114102,12120141114102121,
%T A262641 24012120141114102121042,142401212014111410212104241,
%U A262641 41424012120141114102121042414,314142401212014111410212104241413,4131414240121201411141021210424141314,30413141424012120141114102121042414131403
%N A262641 Minimal nested palindromic base-5 primes with seed 1; see Comments.
%C A262641 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 A262641 Clark Kimberling, <a href="/A262641/b262641.txt">Table of n, a(n) for n = 1..300</a>
%e A262641 a(3) = 41114 is the least base-5 prime having a(2) = 111 in its middle.
%e A262641 Triangular format:
%e A262641            1
%e A262641           111
%e A262641          41114
%e A262641         1411141
%e A262641       20141114102
%e A262641    12120141114102121
%e A262641 24012120141114102121042
%t A262641 s = {1}; base = 5; z = 20; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#, base]], base]] &];
%t A262641 AppendTo[s, FromDigits[IntegerDigits[tmp, base]]], {z}]; s  (* A262641 *)
%t A262641 Map[FromDigits[ToString[#], base] &, s]  (* A262642 *)
%t A262641 (* _Peter J. C. Moses_, Sep 01 2015 *)
%Y A262641 Cf. A261881 (base 10), A262627, A262642.
%K A262641 nonn,easy,base
%O A262641 1,2
%A A262641 _Clark Kimberling_, Oct 24 2015