A262657 Minimal nested palindromic base-7 primes with seed 1; see Comments.

1, 212, 42124, 204212402, 2220421240222, 222204212402222, 2222220421240222222, 12222222042124022222221, 3122222220421240222222213, 331222222204212402222222133, 53312222222042124022222221335, 165331222222204212402222222133561

Offset: 1

Author

Clark Kimberling, Oct 27 2015

Keywords

• nonn
• easy
• base

Comments

Using only base-7 digits 0,1,2,3,4,5,6 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-7 primes with seed s.

Examples

			a(3) = 42124 is the least base-7 prime having a(2) = 212 in its middle. Triangular format:
         1
        212
       42124
     204212402
   2220421240222
  222204212402222
2222220421240222222
		

Links

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

Crossrefs

Cf. A261881 (base 10), A262658, A262627.

Programs

Mathematica

s = {1}; base = 7; 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  (* A262657 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262658 *)
(* Peter J. C. Moses, Sep 01 2015 *)