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%I #8 Oct 26 2015 22:23:35
%S 2,323,3332333,333323333,33333233333,103333323333301,
%T 1210333332333330121,100212103333323333301212001,
%U 3310021210333332333330121200133,3303310021210333332333330121200133033,11330331002121033333233333012120013303311
%N Minimal nested palindromic base-4 primes with seed 2; see Comments.
%C 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 Clark Kimberling, <a href="/A262637/b262637.txt">Table of n, a(n) for n = 1..300</a>
%e a(3) = 3332333 is the least base-4 prime having a(2) = 323 in its middle.
%e Triangular format:
%e 2
%e 323
%e 3332333
%e 333323333
%e 33333233333
%e 103333323333301
%e 1210333332333330121
%t s = {2}; base = 4; 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 (* A262637 *)
%t Map[FromDigits[ToString[#], base] &, s] (* A262638 *)
%t (* _Peter J. C. Moses_, Sep 01 2015 *)
%Y Cf. A261881 (base 10), A262638, A262627.
%K nonn,easy,base
%O 1,1
%A _Clark Kimberling_, Oct 24 2015
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