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A262627 Minimal nested base-2 palindromic primes with seed 0. 19
0, 101, 11001010011, 101100101001101, 10101011001010011010101, 111010101100101001101010111, 1111101010110010100110101011111, 101111111010101100101001101010111111101, 110101111111010101100101001101010111111101011 (list; graph; refs; listen; history; text; internal format)
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: A262645 A138826 A138720 * A259199 A006064 A230304

Adjacent sequences:  A262624 A262625 A262626 * A262628 A262629 A262630

KEYWORD

nonn,base

AUTHOR

Clark Kimberling, Oct 02 2015

STATUS

approved

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Last modified March 23 04:34 EDT 2017. Contains 283902 sequences.