A262655 Minimal nested palindromic base-6 primes with seed 5; see Comments.

5, 151, 11511, 5115115, 13511511531, 5135115115315, 15513511511531551, 1155135115115315511, 14115513511511531551141, 131411551351151153155114131, 51314115513511511531551141315, 11551314115513511511531551141315511, 11511551314115513511511531551141315511511

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) = 11511 is the least base-6 prime having a(2) = 151 in its middle.
Triangular format:
        5
       151
      11511
     5115115
   13511511531
  5135115115315
		

Links

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

Crossrefs

Cf. A261881 (base 10), A262656, A262627.

Programs

Mathematica

s = {5}; 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  (* A262655 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262656 *)
(* Peter J. C. Moses, Sep 01 2015 *)