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%I #8 Oct 26 2015 22:24:00
%S 3,131,11311,121131121,1212113112121,312121131121213,
%T 101312121131121213101,11131013121211311212131013111,
%U 31311131013121211311212131013111313,1011313111310131212113112121310131113131101,310113131113101312121131121213101311131311013
%N Minimal nested palindromic base-4 primes with seed 3; 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="/A262639/b262639.txt">Table of n, a(n) for n = 1..300</a>
%e a(3) = 11311 is the least base-4 prime having a(2) = 131 in its middle.
%e Triangular format:
%e 3
%e 131
%e 11311
%e 121131121
%e 1212113112121
%e 312121131121213
%t s = {3}; 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 (* A262639 *)
%t Map[FromDigits[ToString[#], base] &, s] (* A262640 *)
%t (* _Peter J. C. Moses_, Sep 01 2015 *)
%Y Cf. A261881 (base 10), A262640, A262627.
%K nonn,easy,base
%O 1,1
%A _Clark Kimberling_, Oct 24 2015
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