A262631 Minimal nested base-3 palindromic primes with seed 1.

1, 111, 1111111, 22111111122, 1221111111221, 112211111112211, 2111221111111221112, 2102111221111111221112012, 1212102111221111111221112012121, 20121210211122111111122111201212102, 2002201212102111221111111221112012121022002

Offset: 1

Author

Clark Kimberling, Oct 02 2015

Keywords

• nonn
• base

Comments

Using only base-3 digits 0,1,2, 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 base-3 palindromic primes with seed s.

Examples

			a(4) = 22111111122 is the least base-3 prime having a(3) = 1111111 in its middle. Triangular format:
         1
        111
      1111111
    22111111122
   1221111111221
  112211111112211
		

Links

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

Crossrefs

Cf. A261881 (base 10), A262632, A262627. Subset of A117698 (except a(1)).

Programs

Mathematica

s = {1}; base = 3; 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  (* A262631 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262632 *)
(* Peter J. C. Moses, Sep 01 2015 *)