A262639 Minimal nested palindromic base-4 primes with seed 3; see Comments.

3, 131, 11311, 121131121, 1212113112121, 312121131121213, 101312121131121213101, 11131013121211311212131013111, 31311131013121211311212131013111313, 1011313111310131212113112121310131113131101, 310113131113101312121131121213101311131311013

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) = 11311 is the least base-4 prime having a(2) = 131 in its middle.
Triangular format:
         3
        131
       11311
     121131121
   1212113112121
  312121131121213
		

Links

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

Crossrefs

Cf. A261881 (base 10), A262640, A262627.

Programs

Mathematica

s = {3}; 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  (* A262639 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262640 *)
(* Peter J. C. Moses, Sep 01 2015 *)