A262636 -id:A262636 - cp's OEIS frontend

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

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

Offset: 1

Clark Kimberling, Oct 02 2015

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.
       0      A262627        A262628
       1      A262629        A262630
       1      A262631        A262632
       0      A262633        A262634
       1      A262635        A262636
       2      A262637        A262638
       3      A262639        A262640
       1      A262641        A262642
       3      A262643        A262644
       0      A262645        A262646
       1      A262647        A262648
       2      A262649        A262650
       3      A262651        A262652
       4      A262653        A262654
       5      A262655        A262656
       1      A262657        A262658
       0      A262659        A262660
       1      A262661        A262662
      0      A261881        A261881
      1      A261818        A261818

			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

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

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

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 *)

A262635 Minimal nested base-4 palindromic primes with seed 1.

Original entry on oeis.org

1, 12121, 111212111, 31112121113, 133111212111331, 123133111212111331321, 303123133111212111331321303, 3030312313311121211133132130303, 30303031231331112121113313213030303, 3303030312313311121211133132130303033, 11330303031231331112121113313213030303311

Offset: 1

Clark Kimberling, Oct 02 2015

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.

			a(3) = 111212111 is the least base-4 prime having a(2) = 12121 in its middle. Triangular format:
          1
        12121
      111212111
     31112121113
   133111212111331
123133111212111331321

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

Cf. A261881 (base 10), A262636, A262627. Subsequence of A117699.

s = {1}; 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  (* A262635 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262636 *)
(* Peter J. C. Moses, Sep 01 2015 *)

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

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