A262629 Minimal nested base-2 palindromic primes with seed 1.

1, 111, 11111, 1111111, 1001111111001, 1001001111111001001, 111110010011111110010011111, 111111110010011111110010011111111, 100111111110010011111110010011111111001, 1011010011111111001001111111001001111111100101101

Offset: 1

Author

Clark Kimberling, Oct 02 2015

Keywords

• nonn
• base

Comments

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

Examples

			a(5) = 1001111111001 = A117697(20) is the least base-2 prime having a(4) = 1111111 = A117697(8) in its middle. Triangular format:
             1
            111
           11111
          1111111
       1001111111001
    1001001111111001001
111110010011111110010011111
		

Links

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

Crossrefs

Cf. A261881 (base 10), A262627. Subsequence of A117697 (expect a(1)).

Programs

Mathematica

s = {1}; base = 2; 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  (* A262629 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262630 *)
(* Peter J. C. Moses, Sep 01 2015 *)