A262635 - OEIS

%I #9 Oct 23 2015 13:42:06

%S 1,12121,111212111,31112121113,133111212111331,123133111212111331321,

%T 303123133111212111331321303,3030312313311121211133132130303,

%U 30303031231331112121113313213030303,3303030312313311121211133132130303033,11330303031231331112121113313213030303311

%N Minimal nested base-4 palindromic primes with seed 1.

%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 base-4 palindromic primes with seed s.

%H Clark Kimberling, <a href="/A262635/b262635.txt">Table of n, a(n) for n = 1..300</a>

%e a(3) = 111212111 is the least base-4 prime having a(2) = 12121 in its middle. Triangular format:

%e           1

%e         12121

%e       111212111

%e      31112121113

%e    133111212111331

%e 123133111212111331321

%t s = {1}; 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  (* A262635 *)

%t Map[FromDigits[ToString[#], base] &, s]  (* A262636 *)

%t (* _Peter J. C. Moses_, Sep 01 2015 *)

%Y Cf. A261881 (base 10), A262636, A262627. Subsequence of A117699.

%K nonn,base

%O 1,2

%A _Clark Kimberling_, Oct 02 2015