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 1-5 of 5 results.

A023220 Primes p such that 5*p + 8 is also prime.

Original entry on oeis.org

3, 7, 13, 19, 31, 37, 43, 61, 73, 103, 127, 163, 211, 223, 229, 241, 283, 307, 331, 337, 349, 373, 397, 409, 421, 439, 457, 499, 541, 631, 661, 673, 691, 727, 733, 757, 769, 787, 829, 853, 883, 919, 997, 1021, 1063, 1087, 1123, 1129, 1213, 1231, 1447, 1543, 1549
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Except for the first term all others are congruent to 1 (mod 6) because 5*(6*n+5)+8 is divisible by 3. - Zak Seidov, Aug 23 2012

Links

Crossrefs

Cf. A002476, A111225 (supersequence).

Programs

  • Magma
    [n: n in [0..1000] | IsPrime(n) and IsPrime(5*n+8)]; // Vincenzo Librandi, Nov 20 2010
  • Mathematica
    Select[Prime[Range[250]],PrimeQ[5#+8]&] (* Harvey P. Dale, Apr 21 2020 *)

A023255 Primes that remain prime through 2 iterations of the function f(x) = 5x + 8.

Original entry on oeis.org

7, 13, 19, 31, 43, 73, 211, 223, 241, 307, 397, 409, 631, 661, 727, 757, 769, 829, 883, 1123, 1741, 1783, 1867, 2131, 2143, 2269, 2287, 2467, 2521, 2551, 2857, 2917, 3253, 3319, 3793, 3967, 4297, 4423, 4597, 4957, 5449, 5563, 5701, 6229, 6427, 6469, 6679
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 5*p+8 and 25*p+48 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023220, A111225.

Programs

  • Magma
    [n: n in [0..100000] | IsPrime(n) and IsPrime(5*n+8) and IsPrime(25*n+48)] // Vincenzo Librandi, Aug 04 2010
  • Mathematica
    fQ[n_]:=And@@PrimeQ[NestList[5#+8&,n,2]]; Select[Range[7000],fQ] (* Harvey P. Dale, Mar 25 2013 *)

Formula

a(n) == 1 (mod 6). - John Cerkan, Sep 14 2016

A023286 Primes that remain prime through 3 iterations of function f(x) = 5x + 8.

Original entry on oeis.org

7, 13, 43, 223, 757, 883, 2143, 2269, 2521, 2917, 3253, 3967, 4297, 4423, 6229, 6427, 6679, 7621, 7741, 10429, 11353, 12739, 14593, 14929, 15259, 15541, 15937, 16981, 17449, 17911, 21187, 23899, 24697, 25633, 27481, 28789, 29611, 29833, 30253, 30703
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 5*p+8, 25*p+48 and 125*p+248 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023220, A023255, and A111225.

Programs

  • Magma
    [n: n in [1..150000] | IsPrime(n) and IsPrime(5*n+8) and IsPrime(25*n+48) and IsPrime(125*n+248)] // Vincenzo Librandi, Aug 04 2010
  • Mathematica
    it3Q[n_]:=AllTrue[Rest[NestList[5#+8&,n,3]],PrimeQ]; Select[ Prime[ Range[ 3500]],it3Q] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 21 2015 *)

Formula

a(n) == 1 (mod 6). - John Cerkan, Sep 21 2016

A023316 Primes that remain prime through 4 iterations of function f(x) = 5x + 8.

Original entry on oeis.org

7, 43, 883, 2269, 2917, 7621, 15541, 15937, 36541, 38113, 54787, 60961, 67033, 71359, 77491, 79693, 82531, 84967, 112621, 129589, 176461, 185683, 192547, 239671, 248071, 267373, 271489, 271549, 310231, 316471, 340957, 343267, 350617, 382303
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 5*p+8, 25*p+48, 125*p+248 and 625*p+1248 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023220, A023255, A023286, and A111225.

Programs

  • Magma
    [n: n in [1..1000000] | IsPrime(n) and IsPrime(5*n+8) and IsPrime(25*n+48) and IsPrime(125*n+248) and IsPrime(625*n+1248)] // Vincenzo Librandi, Aug 04 2010
  • PARI
    is(n)=isprime(n) && isprime(5*n+8) && isprime(25*n+48) && isprime(125*n+248) && isprime(625*n+1248) \\ Charles R Greathouse IV, Oct 08 2016

Formula

a(n) == 1 or 19 (mod 42) for n > 1. - John Cerkan, Oct 07 2016

A023344 Primes that remain prime through 5 iterations of function f(x) = 5x + 8.

Original entry on oeis.org

7, 7621, 15937, 382933, 462271, 518803, 866941, 1025407, 1142503, 1427347, 1742473, 1980067, 2343619, 2910031, 3015283, 4344121, 4352269, 4544209, 5081893, 5116543, 5127043, 5482531, 5484379, 5501473, 5648221, 6452899, 7213897, 7968469
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 5*p+8, 25*p+48, 125*p+248, 625*p+1248 and 3125*p+6248 are also primes. - Vincenzo Librandi, Aug 05 2010

Links

Crossrefs

Subsequence of A023220, A023255, A023286, A023316, and A111225.

Programs

  • Magma
    [n: n in [1..10000000] | IsPrime(n) and IsPrime(5*n+8) and IsPrime(25*n+48) and IsPrime(125*n+248) and IsPrime(625*n+1248) and IsPrime(3125*n+6248)] // Vincenzo Librandi, Aug 05 2010
  • Mathematica
    Select[Prime[Range[550000]],And@@PrimeQ[NestList[5#+8&,#,5]]&] (* Harvey P. Dale, Jun 04 2011 *)

Formula

a(n) == 19 (mod 42) for n > 1. - John Cerkan, Oct 22 2016
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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