A262633 Minimal nested base-4 palindromic primes with seed 0.

0, 101, 31013, 3310133, 1023310133201, 3331023310133201333, 3223331023310133201333223, 1133223331023310133201333223311, 100311332233310233101332013332233113001, 10231003113322333102331013320133322331130013201

Offset: 1

Author

Clark Kimberling, Oct 02 2015

Keywords

• nonn
• base

Comments

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

Examples

			a(3) = 31013 is the least base-4 prime having a(2) = 101 in its middle. Triangular format:
         0
        101
       31013
      3310133
   1023310133201
3331023310133201333,
		

Links

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

Crossrefs

Cf. A261881 (base 10), A262634, A262627. Subsequence of A117699.

Programs

Mathematica

s = {0}; base = 4; 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  (* A262633 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262634 *)
(* Peter J. C. Moses, Sep 01 2015 *)