A261881 -id:A261881 - cp's OEIS frontend

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

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 *)

A262643 Minimal nested palindromic base-5 primes with seed 3; see Comments.

Original entry on oeis.org

3, 131, 31313, 1313131, 413131314, 2341313131432, 40234131313143204, 144023413131314320441, 2314402341313131432044132, 2202314402341313131432044132022, 14220231440234131313143204413202241, 20114220231440234131313143204413202241102

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) = 31313 is the least base-5 prime having a(2) = 131 in its middle.
Triangular format:
      3
     131
    31313
   1313131
  413131314
2341313131432

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

Cf. A261881 (base 10), A262644, A262627.

s = {3}; 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  (* A262643 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262644 *)
(* Peter J. C. Moses, Sep 01 2015 *)

A262647 Minimal nested palindromic base-6 primes with seed 1; see Comments.

Original entry on oeis.org

1, 111, 1111111, 14111111141, 111411111114111, 103111411111114111301, 5510311141111111411130155, 10551031114111111141113015501, 501055103111411111114111301550105, 102501055103111411111114111301550105201, 5110250105510311141111111411130155010520115

Offset: 1

Clark Kimberling, Oct 25 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) = 1111111 is the least base-6 prime having a(2) = 111 in its middle. Triangular format:
          1
         111
       1111111
     14111111141
   111411111114111
103111411111114111301

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

Cf. A261881 (base 10), A262648, A262627.

s = {1}; 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  (* A262647 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262648 *)
(* Peter J. C. Moses, Sep 01 2015 *)

A262649 Minimal nested palindromic base-6 primes with seed 2; see Comments.

Original entry on oeis.org

2, 525, 1252521, 512525215, 102512525215201, 5110251252521520115, 151102512525215201151, 5515110251252521520115155, 50551511025125252152011515505, 525055151102512525215201151550525, 1152505515110251252521520115155052511

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) = 1252521 is the least base-6 prime having a(2) = 525 in its middle. Triangular format:
         2
        525
      1252521
     512525215
  102512525215201
5110251252521520115

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

Cf. A261881 (base 10), A262650, A262627.

s = {2}; 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  (* A262649 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262650 *)
(* Peter J. C. Moses, Sep 01 2015 *)

A262653 Minimal nested palindromic base-6 primes with seed 4; see Comments.

Original entry on oeis.org

4, 141, 11411, 5114115, 551141155, 1455114115541, 1111455114115541111, 55111145511411554111155, 1021551111455114115541111551201, 12102155111145511411554111155120121, 531210215511114551141155411115512012135, 101531210215511114551141155411115512012135101

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) = 11411 is the least base-6 prime having a(2) = 141 in its middle. Triangular format:
      4
     141
    11411
   5114115
  551141155
1455114115541

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

Cf. A261881 (base 10), A262654, A262627.

s = {4}; 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  (* A262653 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262654 *)
(* Peter J. C. Moses, Sep 01 2015 *)

A262655 Minimal nested palindromic base-6 primes with seed 5; see Comments.

Original entry on oeis.org

5, 151, 11511, 5115115, 13511511531, 5135115115315, 15513511511531551, 1155135115115315511, 14115513511511531551141, 131411551351151153155114131, 51314115513511511531551141315, 11551314115513511511531551141315511, 11511551314115513511511531551141315511511

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) = 11511 is the least base-6 prime having a(2) = 151 in its middle.
Triangular format:
        5
       151
      11511
     5115115
   13511511531
  5135115115315

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

Cf. A261881 (base 10), A262656, A262627.

s = {5}; 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  (* A262655 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262656 *)
(* Peter J. C. Moses, Sep 01 2015 *)

A262657 Minimal nested palindromic base-7 primes with seed 1; see Comments.

Original entry on oeis.org

1, 212, 42124, 204212402, 2220421240222, 222204212402222, 2222220421240222222, 12222222042124022222221, 3122222220421240222222213, 331222222204212402222222133, 53312222222042124022222221335, 165331222222204212402222222133561

Offset: 1

Clark Kimberling, Oct 27 2015

Using only base-7 digits 0,1,2,3,4,5,6 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-7 primes with seed s.

			a(3) = 42124 is the least base-7 prime having a(2) = 212 in its middle. Triangular format:
         1
        212
       42124
     204212402
   2220421240222
  222204212402222
2222220421240222222

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

Cf. A261881 (base 10), A262658, A262627.

s = {1}; base = 7; 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  (* A262657 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262658 *)
(* Peter J. C. Moses, Sep 01 2015 *)

A262659 Minimal nested palindromic base-8 primes with seed 0; see Comments.

Original entry on oeis.org

0, 13031, 511303115, 3351130311533, 333511303115333, 1033351130311533301, 1051033351130311533301501, 35105103335113031153330150153, 12135105103335113031153330150153121, 12012135105103335113031153330150153121021, 331201213510510333511303115333015015312102133

Offset: 1

Clark Kimberling, Oct 27 2015

Using only base-8 digits 0,1,2,3,4,5,6,7 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-8 primes with seed s.

			a(3) = 511303115 is the least base-8 prime having a(2) = 13031 in its middle. Triangular format:
         0
       13031
     511303115
   3351130311533
  333511303115333
1033351130311533301

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

Cf. A261881 (base 10), A262660, A262627.

s = {0}; base = 8; 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  (* A262659 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262660 *)
(* Peter J. C. Moses, Sep 01 2015 *)

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

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

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

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A262643 Minimal nested palindromic base-5 primes with seed 3; see Comments.

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A262647 Minimal nested palindromic base-6 primes with seed 1; see Comments.

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A262649 Minimal nested palindromic base-6 primes with seed 2; see Comments.

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A262653 Minimal nested palindromic base-6 primes with seed 4; see Comments.

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A262655 Minimal nested palindromic base-6 primes with seed 5; see Comments.

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