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%I #6 Oct 31 2015 15:03:18
%S 4,141,11411,5114115,551141155,1455114115541,1111455114115541111,
%T 55111145511411554111155,1021551111455114115541111551201,
%U 12102155111145511411554111155120121,531210215511114551141155411115512012135,101531210215511114551141155411115512012135101
%N Minimal nested palindromic base-6 primes with seed 4; see Comments.
%C Using only base-6 digits 0,1,2,3,4,5, 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-6 primes with seed s.
%H Clark Kimberling, <a href="/A262653/b262653.txt">Table of n, a(n) for n = 1..300</a>
%e a(3) = 11411 is the least base-6 prime having a(2) = 141 in its middle. Triangular format:
%e 4
%e 141
%e 11411
%e 5114115
%e 551141155
%e 1455114115541
%t s = {4}; base = 6; z = 20; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#, base]], base]] &];
%t AppendTo[s, FromDigits[IntegerDigits[tmp, base]]], {z}]; s (* A262653 *)
%t Map[FromDigits[ToString[#], base] &, s] (* A262654 *)
%t (* _Peter J. C. Moses_, Sep 01 2015 *)
%Y Cf. A261881 (base 10), A262654, A262627.
%K nonn,easy,base
%O 1,1
%A _Clark Kimberling_, Oct 27 2015
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