cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 31-36 of 36 results.

A262497 Minimal nested palindromic primes with seed 11111.

Original entry on oeis.org

11111, 121111121, 71211111217, 3712111112173, 98371211111217389, 129837121111121738921, 3312983712111112173892133, 1063312983712111112173892133601, 12106331298371211111217389213360121, 781210633129837121111121738921336012187
Offset: 1

Views

Author

Clark Kimberling, Sep 24 2015

Keywords

Comments

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.

Examples

			As a triangle:
             11111
           121111121
          71211111217
         3712111112173
       98371211111217389
     129837121111121738921
   3312983712111112173892133
1063312983712111112173892133601

Links

Crossrefs

Cf. A261881.

Programs

  • Mathematica
    s0 = "11111"; 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 *)

A262498 Minimal nested palindromic primes with seed 1111111.

Original entry on oeis.org

1111111, 14111111141, 131411111114131, 91314111111141319, 389131411111114131983, 7238913141111111413198327, 16723891314111111141319832761, 381672389131411111114131983276183, 1638167238913141111111413198327618361, 1191638167238913141111111413198327618361911
Offset: 1

Views

Author

Clark Kimberling, Sep 24 2015

Keywords

Comments

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.

Examples

			As a triangle:
             1111111
           14111111141
         131411111114131
        91314111111141319
      389131411111114131983
    7238913141111111413198327
  16723891314111111141319832761
381672389131411111114131983276183

Links

Crossrefs

Cf. A261881.

Programs

  • Mathematica
    s0 = "1111111"; 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 *)

A262499 Minimal nested palindromic primes with seed 111111111.

Original entry on oeis.org

111111111, 1311111111131, 31131111111113113, 3311311111111131133, 333113111111111311333, 3033311311111111131133303, 1323033311311111111131133303231, 313230333113111111111311333032313, 9531323033311311111111131133303231359
Offset: 1

Views

Author

Clark Kimberling, Sep 24 2015

Keywords

Comments

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.

Examples

			As a triangle:
              111111111
            1311111111131
          31131111111113113
         3311311111111131133
        333113111111111311333
      3033311311111111131133303
   1323033311311111111131133303231
  313230333113111111111311333032313

Links

Crossrefs

Cf. A261881.

Programs

  • Mathematica
    s0 = "111111111"; 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 *)

A262531 Minimal nested palindromic primes with seed 000.

Original entry on oeis.org

1300031, 10130003101, 171013000310171, 91710130003101719, 3917101300031017193, 16391710130003101719361, 10116391710130003101719361101, 191011639171013000310171936110191, 91910116391710130003101719361101919, 119191011639171013000310171936110191911
Offset: 2

Views

Author

Clark Kimberling, Sep 24 2015

Keywords

Comments

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 A261819, the seed is not an integer, so that the offset is 2.)

Examples

			As a triangle:
          000
        1300031
      10130003101
    171013000310171
   91710130003101719
  3917101300031017193
16391710130003101719361

Links

Crossrefs

Cf. A261881.

Programs

  • Mathematica
    s0 = "000"; 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 *)

A262532 Minimal nested palindromic primes with seed 00000.

Original entry on oeis.org

140000041, 31400000413, 9314000004139, 74931400000413947, 3749314000004139473, 937493140000041394739, 3693749314000004139473963, 10369374931400000413947396301, 351036937493140000041394739630153, 7035103693749314000004139473963015307
Offset: 2

Views

Author

Clark Kimberling, Sep 24 2015

Keywords

Comments

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 A252532, the seed is not an integer, so that the offset is 2.)

Examples

			As a triangle:
          00000
        140000041
       31400000413
      9314000004139
    74931400000413947
   3749314000004139473
  937493140000041394739

Links

Crossrefs

Cf. A261881.

Programs

  • Mathematica
    s0 = "00000"; 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 *)

A262533 Minimal nested palindromic primes with seed 0000000.

Original entry on oeis.org

19000000091, 1190000000911, 36119000000091163, 953611900000009116359, 9095361190000000911635909, 790953611900000009116359097, 1479095361190000000911635909741, 72147909536119000000091163590974127, 10572147909536119000000091163590974127501
Offset: 2

Views

Author

Clark Kimberling, Sep 24 2015

Keywords

Comments

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 A260444, the seed is not an integer, so that the offset is 2.)

Examples

			As a triangle:
            0000000
          19000000091
         1190000000911
       36119000000091163
     953611900000009116359
   9095361190000000911635909
  790953611900000009116359097

Links

Crossrefs

Cf. A261881.

Programs

  • Mathematica
    s0 = "0000000"; 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 *)
Previous Showing 31-36 of 36 results.

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