A261881 -id:A261881 - cp's OEIS frontend

A262661 Minimal nested palindromic base-8 primes with seed 1; see Comments.

1, 111, 1411141, 12141114121, 10412141114121401, 11610412141114121401611, 171161041214111412140161171, 303171161041214111412140161171303, 3230317116104121411141214016117130323, 71323031711610412141114121401611713032317

Offset: 1

Clark Kimberling, Oct 31 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) = 1411141 is the least base-8 prime having a(2) = 111 in its middle. Triangular format:
           1
          111
        1411141
      12141114121
   10412141114121401
11610412141114121401611

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

Cf. A261881 (base 10), A262662, A262627.

s = {1}; 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  (* A262661 *)
Map[FromDigits[ToString[#], base] &, s]  (* A262662 *)
(* Peter J. C. Moses, Sep 01 2015 *)

A260250 Minimal nested palindromic primes with seed 000000000.

Original entry on oeis.org

1300000000031, 713000000000317, 1471300000000031741, 12147130000000003174121, 3121471300000000031741213, 1213121471300000000031741213121, 33121312147130000000003174121312133, 323312131214713000000000317412131213323

Offset: 2

Clark Kimberling, Sep 24 2015

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 having a(n-1) in the middle. Then (a(n)) is the sequence of minimal nested palindromic primes with seed s. (For A260250, the seed is not an integer, so that the offset is 2.)

			As a triangle:
           000000000
         1300000000031
        713000000000317
      1471300000000031741
    12147130000000003174121,
   3121471300000000031741213
1213121471300000000031741213121,

Clark Kimberling, Table of n, a(n) for n = 2..200

Cf. A261881.

s0 = "000000000"; s = {ToExpression[s0]};Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s], 10, Max[StringLength[s0],Length[IntegerDigits[Last[s]]]]], Reverse[#]]&[IntegerDigits[#]]]] &]; AppendTo[s, tmp], {10}]; s0 <> ", " <> StringTake[ToString[Rest[s]], {2, -2}]
(* Peter J. C. Moses, Sep 23 2015 *)

A260459 Minimal nested palindromic primes with seed 010.

Original entry on oeis.org

30103, 333010333, 33330103333, 9333301033339, 12933330103333921, 121293333010333392121, 3812129333301033339212183, 15381212933330103333921218351, 101538121293333010333392121835101, 3910153812129333301033339212183510193

Offset: 2

Clark Kimberling, Sep 24 2015

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 having a(n-1) in the middle. Then (a(n)) is the sequence of minimal nested palindromic primes with seed s. (For A260459, the seed is not an integer, so that the offset is 2.)

			As a triangle:
           010
          30103
        333010333
       33330103333
      9333301033339
    12933330103333921
  121293333010333392121
3812129333301033339212183

Cf. A261881.

s0 = "010"; s = {ToExpression[s0]};Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s], 10, Max[StringLength[s0],Length[IntegerDigits[Last[s]]]]], Reverse[#]]&[IntegerDigits[#]]]] &]; AppendTo[s, tmp], {10}]; s0 <> ", " <> StringTake[ToString[Rest[s]], {2, -2}]
(* Peter J. C. Moses, Sep 23 2015 *)

A261820 Minimal nested palindromic primes with seed 111.

Original entry on oeis.org

111, 1311131, 113111311, 91131113119, 9911311131199, 12991131113119921, 771299113111311992177, 1077129911311131199217701, 11107712991131113119921770111, 101110771299113111311992177011101, 107101110771299113111311992177011101701

Offset: 1

Clark Kimberling, Sep 24 2015

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 having a(n-1) in the middle. Then (a(n)) is the sequence of minimal nested palindromic primes with seed s.

			As a triangle:
        111
      1311131
     113111311
    91131113119
   9911311131199
  12991131113119921
771299113111311992177

Clark Kimberling, Table of n, a(n) for n = 1..200

Cf. A261881.

s0 = "111"; s = {ToExpression[s0]};Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s], 10, Max[StringLength[s0],Length[IntegerDigits[Last[s]]]]], Reverse[#]]&[IntegerDigits[#]]]] &]; AppendTo[s, tmp], {10}]; s0 <> ", " <> StringTake[ToString[Rest[s]], {2, -2}]
(* Peter J. C. Moses, Sep 23 2015 *)

A261821 Minimal nested palindromic primes with seed 4.

Original entry on oeis.org

4, 11411, 1114111, 18111411181, 741811141118147, 1674181114111814761, 90167418111411181476109, 3901674181114111814761093, 14390167418111411181476109341, 9143901674181114111814761093419, 75914390167418111411181476109341957

Offset: 1

Clark Kimberling, Sep 23 2015

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 primes with seed s.

			As a triangle:
.........4
.......11411
......1114111
....18111411181
..741811141118147
1674181114111814761

Clark Kimberling, Table of n, a(n) for n = 1..200

Cf. A261881 (seed 0, with guide to related sequences).

s = {4}; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#]]]] &]; AppendTo[s, tmp], {15}]; s
(* Peter J. C. Moses, Sep 01 2015 *)

A261822 Minimal nested palindromic primes with seed 5.

Original entry on oeis.org

5, 151, 31513, 3315133, 11331513311, 191133151331191, 9919113315133119199, 39991911331513311919993, 353999191133151331191999353, 13539991911331513311919993531, 741353999191133151331191999353147

Offset: 1

Clark Kimberling, Sep 23 2015

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 primes with seed s.

			As a triangle:
.......5
......151
.....31513
....3315133
..11331513311
191133151331191

Clark Kimberling, Table of n, a(n) for n = 1..200

Cf. A261881 (seed 0, with guide to related sequences).

s = {5}; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#]]]] &]; AppendTo[s, tmp], {15}]; s
(* Peter J. C. Moses, Sep 01 2015 *)

A261823 Minimal nested palindromic primes with seed 6.

Original entry on oeis.org

6, 10601, 3106013, 19310601391, 3193106013913, 30319310601391303, 3303193106013913033, 333031931060139130333, 33330319310601391303333, 303333031931060139130333303, 1130333303193106013913033330311, 19113033330319310601391303333031191

Offset: 1

Clark Kimberling, Sep 23 2015

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 primes with seed s.

			As a triangle:
........6
......10601
.....3106013
...19310601391
..3193106013913
30319310601391303

Clark Kimberling, Table of n, a(n) for n = 1..200

Cf. A261881 (seed 0, with guide to related sequences).

s = {6}; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#]]]] &]; AppendTo[s, tmp], {15}]; s
(* Peter J. C. Moses, Sep 01 2015 *)

A261824 Minimal nested palindromic primes with seed 7.

Original entry on oeis.org

7, 373, 93739, 129373921, 3212937392123, 34321293739212343, 353432129373921234353, 1335343212937392123435331, 1171335343212937392123435331711, 1051171335343212937392123435331711501, 74105117133534321293739212343533171150147

Offset: 1

Clark Kimberling, Sep 23 2015

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 primes with seed s.

			As a triangle:
........7
.......373
......93739
....129373921
..3212937392123
34321293739212343

Clark Kimberling, Table of n, a(n) for n = 1..200

Cf. A261881 (seed 0, with guide to related sequences).

s = {7}; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#]]]] &]; AppendTo[s, tmp], {15}]; s
(* Peter J. C. Moses, Sep 01 2015 *)

A261825 Minimal nested palindromic primes with seed 8.

Original entry on oeis.org

8, 181, 1218121, 15121812151, 111512181215111, 3311151218121511133, 133111512181215111331, 1113311151218121511133111, 1141113311151218121511133111411, 73114111331115121812151113311141137, 30273114111331115121812151113311141137203

Offset: 1

Clark Kimberling, Sep 23 2015

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 primes with seed s.

			As a triangle:
.........8
........181
......1218121
....15121812151
..111512181215111
3311151218121511133

Clark Kimberling, Table of n, a(n) for n = 1..200

Cf. A261881 (seed 0, with guide to related sequences).

s = {8}; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#]]]] &]; AppendTo[s, tmp], {15}]; s
(* Peter J. C. Moses, Sep 01 2015 *)

A261826 Minimal nested palindromic primes with seed 9.

Original entry on oeis.org

9, 191, 71917, 147191741, 3914719174193, 139147191741931, 7213914719174193127, 33721391471917419312733, 9337213914719174193127339, 1719337213914719174193127339171, 11171933721391471917419312733917111, 1111719337213914719174193127339171111

Offset: 1

Clark Kimberling, Sep 23 2015

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 primes with seed s.

			As a triangle:
.......9
......191
.....71917
...147191741
.3914719174193
139147191741931

Clark Kimberling, Table of n, a(n) for n = 1..200

Cf. A261881 (seed 0, with guide to related sequences).

s = {9}; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#]]]] &]; AppendTo[s, tmp], {15}]; s
(* Peter J. C. Moses, Sep 01 2015 *)

cp's OEIS Frontend

A262661 Minimal nested palindromic base-8 primes with seed 1; see Comments.

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A260250 Minimal nested palindromic primes with seed 000000000.

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A260459 Minimal nested palindromic primes with seed 010.

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A261820 Minimal nested palindromic primes with seed 111.

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A261821 Minimal nested palindromic primes with seed 4.

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A261822 Minimal nested palindromic primes with seed 5.

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A261823 Minimal nested palindromic primes with seed 6.

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A261824 Minimal nested palindromic primes with seed 7.

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