A262643 Minimal nested palindromic base-5 primes with seed 3; see Comments.

3, 131, 31313, 1313131, 413131314, 2341313131432, 40234131313143204, 144023413131314320441, 2314402341313131432044132, 2202314402341313131432044132022, 14220231440234131313143204413202241, 20114220231440234131313143204413202241102

Offset: 1

Author

Clark Kimberling, Oct 24 2015

Keywords

• nonn
• base

Comments

Using only base-5 digits 0,1,2,3,4, 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-5 primes with seed s.

Examples

			a(3) = 31313 is the least base-5 prime having a(2) = 131 in its middle.
Triangular format:
      3
     131
    31313
   1313131
  413131314
2341313131432
		

Links

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

Crossrefs

Cf. A261881 (base 10), A262644, A262627.

Programs

Mathematica

s = {3}; base = 5; 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  (* A262643 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262644 *)
(* Peter J. C. Moses, Sep 01 2015 *)