A262645 Minimal nested palindromic base-6 primes with seed 0; see Comments.

0, 101, 5110115, 13511011531, 1135110115311, 111351101153111, 152111351101153111251, 5215211135110115311125125, 1025215211135110115311125125201, 1431025215211135110115311125125201341, 1111431025215211135110115311125125201341111

Offset: 1

Author

Clark Kimberling, Oct 24 2015

Keywords

• nonn
• 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) = 5110115 is the least base-6 prime having a(2) = 101 in its middle.
Triangular format:
         0
        101
      5110115
    13511011531
   1135110115311
  111351101153111
		

Links

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

Crossrefs

Cf. A261881 (base 10), A262646, A262627.

Programs

Mathematica

s = {0}; 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  (* A262645 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262646 *)
(* Peter J. C. Moses, Sep 01 2015 *)