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A262649 Minimal nested palindromic base-6 primes with seed 2; see Comments.

%I A262649 #7 Oct 31 2015 15:02:41
%S A262649 2,525,1252521,512525215,102512525215201,5110251252521520115,
%T A262649 151102512525215201151,5515110251252521520115155,
%U A262649 50551511025125252152011515505,525055151102512525215201151550525,1152505515110251252521520115155052511
%N A262649 Minimal nested palindromic base-6 primes with seed 2; see Comments.
%C A262649 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 A262649 Clark Kimberling, <a href="/A262649/b262649.txt">Table of n, a(n) for n = 1..300</a>
%e A262649 a(3) = 1252521 is the least base-6 prime having a(2) = 525 in its middle. Triangular format:
%e A262649          2
%e A262649         525
%e A262649       1252521
%e A262649      512525215
%e A262649   102512525215201
%e A262649 5110251252521520115
%t A262649 s = {2}; base = 6; z = 20; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#, base]], base]] &];
%t A262649 AppendTo[s, FromDigits[IntegerDigits[tmp, base]]], {z}]; s  (* A262649 *)
%t A262649 Map[FromDigits[ToString[#], base] &, s]  (* A262650 *)
%t A262649 (* _Peter J. C. Moses_, Sep 01 2015 *)
%Y A262649 Cf. A261881 (base 10), A262650, A262627.
%K A262649 nonn,easy,base
%O A262649 1,1
%A A262649 _Clark Kimberling_, Oct 27 2015