A262627 Minimal nested base-2 palindromic primes with seed 0.

0, 101, 11001010011, 101100101001101, 10101011001010011010101, 111010101100101001101010111, 1111101010110010100110101011111, 101111111010101100101001101010111111101, 110101111111010101100101001101010111111101011

Offset

1,2

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 -- a(1) being not prime, of course.

Guide to related sequences

base seed base-b repr. base-10 repr.

2 0 A262627 A262628

2 1 A262629 A262630

3 1 A262631 A262632

4 0 A262633 A262634

4 1 A262635 A262636

4 2 A262637 A262638

4 3 A262639 A262640

5 1 A262641 A262642

5 3 A262643 A262644

6 0 A262645 A262646

6 1 A262647 A262648

6 2 A262649 A262650

6 3 A262651 A262652

6 4 A262653 A262654

6 5 A262655 A262656

7 1 A262657 A262658

8 0 A262659 A262660

8 1 A262661 A262662

10 0 A261881 A261881

10 1 A261818 A261818

Links

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

Example

a(3) = 11001010011 =A117697(15) is the least prime having a(2) = 101 in its middle. Triangular format:
               0
              101
          11001010011
        101100101001101
    10101011001010011010101
  111010101100101001101010111
1111101010110010100110101011111

Mathematica

s = {0}; 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  (* A262627 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262628 *)
(* Peter J. C. Moses, Sep 01 2015 *)

Crossrefs

Cf. A117697, A261881 (base 10), A262628-A262662.

Sequence in context: A138826 A292686 A138720 * A259199 A006064 A230304

Adjacent sequences: A262624 A262625 A262626 * A262628 A262629 A262630

Keyword

nonn,base

Author

Clark Kimberling, Oct 02 2015

Status

approved