A262627 -id:A262627 - cp's OEIS frontend

A262628 Base-10 representation of 0 and the primes at A262627.

0, 5, 1619, 22861, 5608661, 123097943, 2103004511, 411605194237, 29681120620523, 8356197277826743, 141511180168198879, 23016765965614427641, 30251327028834944270131, 371385619022538141977254297, 124784413675757116661951994259

Offset: 1

Clark Kimberling, Oct 02 2015

			n   A262627(n)    base-10 representation
1   0                   0
2   101                 5
3   11001010011         1619

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

Cf. A262627. Subsequence of A016041 (except a(1)).

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 *)

A262645 Minimal nested palindromic base-6 primes with seed 0; see Comments.

Original entry on oeis.org

0, 101, 5110115, 13511011531, 1135110115311, 111351101153111, 152111351101153111251, 5215211135110115311125125, 1025215211135110115311125125201, 1431025215211135110115311125125201341, 1111431025215211135110115311125125201341111

Offset: 1

Clark Kimberling, Oct 24 2015

Using only base-6 digits 0,1,2,3,4,5, 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-6 primes with seed s.

			a(3) = 5110115 is the least base-6 prime having a(2) = 101 in its middle.
Triangular format:
         0
        101
      5110115
    13511011531
   1135110115311
  111351101153111

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

Cf. A261881 (base 10), A262646, A262627.

s = {0}; base = 6; 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  (* A262645 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262646 *)
(* Peter J. C. Moses, Sep 01 2015 *)

A262651 Minimal nested palindromic base-6 primes with seed 3; see Comments.

Original entry on oeis.org

3, 11311, 121131121, 5312113112135, 14531211311213541, 1145312113112135411, 51114531211311213541115, 5511145312113112135411155, 50551114531211311213541115505, 115055111453121131121354111550511, 51150551114531211311213541115505115

Offset: 1

Clark Kimberling, Oct 27 2015

Using only base-6 digits 0,1,2,3,4,5, 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-6 primes with seed s.

			a(3) = 121131121 is the least base-6 prime having a(2) = 11311 in its middle. Triangular format:
        3
      11311
    121131121
  5312113112135
14531211311213541

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

Cf. A261881 (base 10), A262652, A262627.

s = {3}; base = 6; 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  (* A262651 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262652 *)
(* Peter J. C. Moses, Sep 01 2015 *)

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

Original entry on oeis.org

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

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(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

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

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

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 *)

A262631 Minimal nested base-3 palindromic primes with seed 1.

Original entry on oeis.org

1, 111, 1111111, 22111111122, 1221111111221, 112211111112211, 2111221111111221112, 2102111221111111221112012, 1212102111221111111221112012121, 20121210211122111111122111201212102, 2002201212102111221111111221112012121022002

Offset: 1

Clark Kimberling, Oct 02 2015

Using only base-3 digits 0,1,2, 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-3 palindromic primes with seed s.

			a(4) = 22111111122 is the least base-3 prime having a(3) = 1111111 in its middle. Triangular format:
         1
        111
      1111111
    22111111122
   1221111111221
  112211111112211

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

Cf. A261881 (base 10), A262632, A262627. Subset of A117698 (except a(1)).

s = {1}; base = 3; 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  (* A262631 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262632 *)
(* Peter J. C. Moses, Sep 01 2015 *)

A262633 Minimal nested base-4 palindromic primes with seed 0.

Original entry on oeis.org

0, 101, 31013, 3310133, 1023310133201, 3331023310133201333, 3223331023310133201333223, 1133223331023310133201333223311, 100311332233310233101332013332233113001, 10231003113322333102331013320133322331130013201

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) = 31013 is the least base-4 prime having a(2) = 101 in its middle. Triangular format:
         0
        101
       31013
      3310133
   1023310133201
3331023310133201333,

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

Cf. A261881 (base 10), A262634, A262627. Subsequence of A117699.

s = {0}; 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  (* A262633 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262634 *)
(* 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 *)

A262637 Minimal nested palindromic base-4 primes with seed 2; see Comments.

Original entry on oeis.org

2, 323, 3332333, 333323333, 33333233333, 103333323333301, 1210333332333330121, 100212103333323333301212001, 3310021210333332333330121200133, 3303310021210333332333330121200133033, 11330331002121033333233333012120013303311

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) = 3332333 is the least base-4 prime having a(2) = 323 in its middle.
Triangular format:
         2
        323
      3332333
     333323333
    33333233333
  103333323333301
1210333332333330121

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

Cf. A261881 (base 10), A262638, A262627.

s = {2}; 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  (* A262637 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262638 *)
(* Peter J. C. Moses, Sep 01 2015 *)

A262641 Minimal nested palindromic base-5 primes with seed 1; see Comments.

Original entry on oeis.org

1, 111, 41114, 1411141, 20141114102, 12120141114102121, 24012120141114102121042, 142401212014111410212104241, 41424012120141114102121042414, 314142401212014111410212104241413, 4131414240121201411141021210424141314, 30413141424012120141114102121042414131403

Offset: 1

Clark Kimberling, Oct 24 2015

Using only base-5 digits 0,1,2,3,4, 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-5 primes with seed s.

			a(3) = 41114 is the least base-5 prime having a(2) = 111 in its middle.
Triangular format:
           1
          111
         41114
        1411141
      20141114102
   12120141114102121
24012120141114102121042

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

Cf. A261881 (base 10), A262627, A262642.

s = {1}; base = 5; 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  (* A262641 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262642 *)
(* Peter J. C. Moses, Sep 01 2015 *)

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A262628 Base-10 representation of 0 and the primes at A262627.

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

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A262645 Minimal nested palindromic base-6 primes with seed 0; see Comments.

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A262651 Minimal nested palindromic base-6 primes with seed 3; see Comments.

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

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A262631 Minimal nested base-3 palindromic primes with seed 1.

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A262633 Minimal nested base-4 palindromic primes with seed 0.

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

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