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.

Showing 1-4 of 4 results.

A117777 Total number of palindromic primes in base 4 below 4^n.

Original entry on oeis.org

2, 3, 6, 6, 16, 16, 45, 45, 142, 142, 435, 435, 1417, 1417, 4802, 4802, 16433, 16433, 57808, 57808, 210708, 210708, 752233, 752233, 2748264, 2748264, 10211513, 10211513, 38013234, 38013234, 140417288, 140417288
Offset: 1

Views

Author

Martin Renner, Apr 15 2006

Keywords

Comments

Every palindrome with an even number of digits is divisible by 11 (in base 4) and therefore is composite (not prime). Hence there is only one palindromic prime with an even number of digits.

Links

Crossrefs

Partial sums of A117778.
Cf. A029972, A117699.
Cf. A117772, A117775, A117779, A117781, A117783, A117785, A117787.

Extensions

a(13)-a(32) from the data at A117778 added by Amiram Eldar, Mar 21 2021

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

Views

Author

Clark Kimberling, Oct 02 2015

Keywords

Comments

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.

Examples

			a(3) = 31013 is the least base-4 prime having a(2) = 101 in its middle. Triangular format:
         0
        101
       31013
      3310133
   1023310133201
3331023310133201333,

Links

Crossrefs

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

Programs

  • Mathematica
    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

Views

Author

Clark Kimberling, Oct 02 2015

Keywords

Comments

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.

Examples

			a(3) = 111212111 is the least base-4 prime having a(2) = 12121 in its middle. Triangular format:
          1
        12121
      111212111
     31112121113
   133111212111331
123133111212111331321

Links

Crossrefs

Cf. A261881 (base 10), A262636, A262627. Subsequence of A117699.

Programs

  • Mathematica
    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 *)

A117778 Total number of palindromic primes in base 4 with n digits.

Original entry on oeis.org

2, 1, 3, 0, 10, 0, 29, 0, 97, 0, 293, 0, 982, 0, 3385, 0, 11631, 0, 41375, 0, 152900, 0, 541525, 0, 1996031, 0, 7463249, 0, 27801721, 0, 102404054, 0
Offset: 1

Views

Author

Martin Renner, Apr 15 2006

Keywords

Comments

Every palindrome with an even number of digits is divisible by 11 (in base 4) and therefore is composite (not prime). Hence there is only one palindromic prime with an even number of digits.

Links

Crossrefs

Cf. A029972, A117699.

Extensions

a(13)-a(32) from Chai Wah Wu, Dec 27 2015
Showing 1-4 of 4 results.

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