A262647 Minimal nested palindromic base-6 primes with seed 1; see Comments.

1, 111, 1111111, 14111111141, 111411111114111, 103111411111114111301, 5510311141111111411130155, 10551031114111111141113015501, 501055103111411111114111301550105, 102501055103111411111114111301550105201, 5110250105510311141111111411130155010520115

Offset: 1

Author

Clark Kimberling, Oct 25 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) = 1111111 is the least base-6 prime having a(2) = 111 in its middle. Triangular format:
          1
         111
       1111111
     14111111141
   111411111114111
103111411111114111301
		

Links

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

Crossrefs

Cf. A261881 (base 10), A262648, A262627.

Programs

Mathematica

s = {1}; 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  (* A262647 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262648 *)
(* Peter J. C. Moses, Sep 01 2015 *)