A262637 Minimal nested palindromic base-4 primes with seed 2; see Comments.

2, 323, 3332333, 333323333, 33333233333, 103333323333301, 1210333332333330121, 100212103333323333301212001, 3310021210333332333330121200133, 3303310021210333332333330121200133033, 11330331002121033333233333012120013303311

Offset: 1

Author

Clark Kimberling, Oct 24 2015

Keywords

• nonn
• easy
• base

Comments

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.

Examples

			a(3) = 3332333 is the least base-4 prime having a(2) = 323 in its middle.
Triangular format:
         2
        323
      3332333
     333323333
    33333233333
  103333323333301
1210333332333330121
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A261881 (base 10), A262638, A262627.

Programs

Mathematica

s = {2}; base = 4; z = 20; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#, base]], base]] &];
AppendTo[s, FromDigits[IntegerDigits[tmp, base]]], {z}]; s  (* A262637 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262638 *)
(* Peter J. C. Moses, Sep 01 2015 *)