A262641 Minimal nested palindromic base-5 primes with seed 1; see Comments.

1, 111, 41114, 1411141, 20141114102, 12120141114102121, 24012120141114102121042, 142401212014111410212104241, 41424012120141114102121042414, 314142401212014111410212104241413, 4131414240121201411141021210424141314, 30413141424012120141114102121042414131403

Offset: 1

Author

Clark Kimberling, Oct 24 2015

Keywords

• nonn
• easy
• 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) = 41114 is the least base-5 prime having a(2) = 111 in its middle.
Triangular format:
           1
          111
         41114
        1411141
      20141114102
   12120141114102121
24012120141114102121042
		

Links

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

Crossrefs

Cf. A261881 (base 10), A262627, A262642.

Programs

Mathematica

s = {1}; 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  (* A262641 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262642 *)
(* Peter J. C. Moses, Sep 01 2015 *)