A262653 Minimal nested palindromic base-6 primes with seed 4; see Comments.

4, 141, 11411, 5114115, 551141155, 1455114115541, 1111455114115541111, 55111145511411554111155, 1021551111455114115541111551201, 12102155111145511411554111155120121, 531210215511114551141155411115512012135, 101531210215511114551141155411115512012135101

Offset: 1

Author

Clark Kimberling, Oct 27 2015

Keywords

• nonn
• easy
• base

Comments

Using only base-6 digits 0,1,2,3,4,5, 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-6 primes with seed s.

Examples

			a(3) = 11411 is the least base-6 prime having a(2) = 141 in its middle. Triangular format:
      4
     141
    11411
   5114115
  551141155
1455114115541
		

Links

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

Crossrefs

Cf. A261881 (base 10), A262654, A262627.

Programs

Mathematica

s = {4}; base = 6; 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  (* A262653 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262654 *)
(* Peter J. C. Moses, Sep 01 2015 *)