A262651 Minimal nested palindromic base-6 primes with seed 3; see Comments.

3, 11311, 121131121, 5312113112135, 14531211311213541, 1145312113112135411, 51114531211311213541115, 5511145312113112135411155, 50551114531211311213541115505, 115055111453121131121354111550511, 51150551114531211311213541115505115

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) = 121131121 is the least base-6 prime having a(2) = 11311 in its middle. Triangular format:
        3
      11311
    121131121
  5312113112135
14531211311213541
		

Links

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

Crossrefs

Cf. A261881 (base 10), A262652, A262627.

Programs

Mathematica

s = {3}; 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  (* A262651 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262652 *)
(* Peter J. C. Moses, Sep 01 2015 *)