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 1-3 of 3 results.

A280720 For p = prime(n), number of iterations of the function f(x) = 5x + 2 that leave p prime.

Original entry on oeis.org

0, 1, 0, 1, 0, 2, 0, 3, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 2, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Felix Fröhlich, Jan 07 2017

Keywords

Comments

Records are a(1) = 0 [p = 2], a(2) = 1 [p = 3], a(6) = 2 [p = 13], a(8) = 3 [p = 19], a(74) = 4 [p = 373], a(12656) = 6 [p = 135859], a(1165346) = 7 [p = 18235423], a(1659004) = 8 [p = 26588257], a(5386789) = 9 [p = 93112729], .... - Charles R Greathouse IV, Jan 12 2017

Links

Crossrefs

Cf. A016873, A023217, A023252, A023283, A023313, A023341, A084958, A249573.

Programs

  • Mathematica
    Table[Length@ NestWhileList[5 # + 2 &, Prime@ n, PrimeQ] - 2, {n, 120}] (* Michael De Vlieger, Jan 09 2017 *)
  • PARI
    a016873(n) = 5*n+2
a(n) = my(p=prime(n), i=0); while(1, if(!ispseudoprime(a016873(p)), return(i), p=a016873(p); i++))

A023313 Primes that remain prime through 4 iterations of function f(x) = 5x + 2.

Original entry on oeis.org

373, 1171, 13687, 21997, 25657, 61603, 74413, 76471, 84199, 87181, 93487, 114691, 135859, 170761, 174877, 184333, 192979, 196177, 207931, 209743, 244219, 276229, 286687, 292561, 297811, 334603, 338893, 405037, 408361, 417097, 439141, 446323
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 5*p+2, 25*p+12, 125*p+62 and 625*p+312 are also primes. - Vincenzo Librandi, Aug 04 2010
Numbers k such that A280720(k) > 3. - Felix Fröhlich, Jan 07 2017

Links

Crossrefs

Cf. A280720. Subsequence of A023217, A023252, A023283, and A111223.

Programs

  • Magma
    [n: n in [1..1000000] | IsPrime(n) and IsPrime(5*n+2) and IsPrime(25*n+12) and IsPrime(125*n+62) and IsPrime(625*n+312)]; // Vincenzo Librandi, Aug 04 2010
  • Mathematica
    Select[Range[10^6], Times @@ Boole@ Map[PrimeQ, NestList[5 # + 2 &, #, 4]] == 1 &] (* Michael De Vlieger, Jan 09 2017 *)

Formula

a(n) == 31 or 37 (mod 42). - John Cerkan, Oct 07 2016

A023341 Primes that remain prime through 5 iterations of function f(x) = 5x + 2.

Original entry on oeis.org

135859, 174877, 192979, 244219, 292561, 679297, 842341, 964897, 1076029, 1470241, 1990579, 2004943, 2339263, 2615707, 2625577, 2633557, 2892277, 3003787, 3201901, 3758233, 4406797, 5065861, 5157547, 5390857, 5424961, 5546173, 5875369, 7746217
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 5*p+2, 25*p+12, 125*p+62, 625*p+312 and 3125*p+1562 are also primes. - Vincenzo Librandi, Aug 05 2010
Numbers k such that A280720(k) > 4. - Felix Fröhlich, Jan 07 2017

Links

Crossrefs

Subsequence of A023217, A023252, A023283, A023313, and A111223.
Cf. A280720.

Programs

  • Magma
    [n: n in [1..10000000] | IsPrime(n) and IsPrime(5*n+2) and IsPrime(25*n+12) and IsPrime(125*n+62) and IsPrime(625*n+312) and IsPrime(3125*n+1562)] // Vincenzo Librandi, Aug 05 2010
  • Mathematica
    p5Q[n_]:=And@@PrimeQ/@NestList[5#+2&,n,5]
Select[Prime[Range[550000]],p5Q]  (* Harvey P. Dale, Feb 17 2011 *)

Formula

a(n) == 31 (mod 42). - John Cerkan, Oct 17 2016
Showing 1-3 of 3 results.

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

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