A262640 -id:A262640 - 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 *)

A262639 Minimal nested palindromic base-4 primes with seed 3; see Comments.

Original entry on oeis.org

3, 131, 11311, 121131121, 1212113112121, 312121131121213, 101312121131121213101, 11131013121211311212131013111, 31311131013121211311212131013111313, 1011313111310131212113112121310131113131101, 310113131113101312121131121213101311131311013

Offset: 1

Clark Kimberling, Oct 24 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 palindromic base-4 primes with seed s.

			a(3) = 11311 is the least base-4 prime having a(2) = 131 in its middle.
Triangular format:
         3
        131
       11311
     121131121
   1212113112121
  312121131121213

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

Cf. A261881 (base 10), A262640, A262627.

s = {3}; 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  (* A262639 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262640 *)
(* Peter J. C. Moses, Sep 01 2015 *)

A262642 Base-10 representation of 1 and the primes at A262641.

Original entry on oeis.org

1, 31, 2659, 28921, 20254277, 222258347161, 6703502508238897, 2849796577598550571, 163260594826469315359, 78587320839900014133983, 63082726980138277941240209, 28861909227691304085982177103, 17774573388934687063056536849453

Offset: 1

Clark Kimberling, Oct 24 2015

			n   A262641(n)    base-10 representation
1     1                  1
2     111                31
3     41114              2659

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

Cf. A262641.

s = {3}; 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  (* A262639 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262640 *)
(* 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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A262639 Minimal nested palindromic base-4 primes with seed 3; see Comments.

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A262642 Base-10 representation of 1 and the primes at A262641.

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