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.

A087576 Smallest number k > 1 such that k^n+2 is prime.

Original entry on oeis.org

3, 3, 3, 3, 9, 39, 9, 3, 11, 3, 15, 9, 9, 3, 3, 15, 5, 9, 63, 15, 27, 39, 41, 3, 51, 3, 59, 75, 119, 99, 71, 141, 209, 87, 65, 3, 275, 45, 23, 21, 27, 27, 69, 477, 59, 147, 231, 1605, 9, 291, 65, 15, 75, 57, 9, 225, 119, 273, 855, 33, 77, 513, 3, 219, 75, 51, 489, 369
Offset: 1

Views

Author

Amarnath Murthy, Sep 17 2003

Keywords

Comments

Some of the results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 16 2019

Links

Crossrefs

Cf. A095302 (corresponding primes), A095303 (smallest k such that k^n-2 is prime), A095304 (corresponding primes).

Programs

  • Mathematica
    Table[k = 2; While[p = k^n + 2; ! PrimeQ[p], k++]; k, {n, 68}] (* T. D. Noe, Apr 03 2012 *)
  • PARI
    for(n=1,68,forstep(k=3,oo,2,if(isprime(k^n+2),print1(k,", ");break))) \\ Hugo Pfoertner, Oct 30 2018

Extensions

Corrected and extended by Hugo Pfoertner, computed using PFGW, Jun 01 2004
a(49) corrected by T. D. Noe, Apr 03 2012

A095304 Smallest prime of the form k^n-2.

Original entry on oeis.org

2, 2, 727, 79, 241, 727, 823541, 5764799, 19681, 16679880978199, 31381059607, 13841287199, 42052983462257057, 6103515623, 4747561509941, 28644003124274380508351359, 98526125335693359373, 136753052840548005895349735207879, 22168378200531005859373
Offset: 1

Views

Author

Hugo Pfoertner, Jun 01 2004

Keywords

Examples

			a(7)=7^7-2=823541 is prime whereas 3^7-2=2185 and 5^7-2=78123 are composite.

Links

Crossrefs

Cf. A095303 (smallest k such that k^n-2 is prime), A087576 (smallest k such that k^n+2 is prime), A095302 (corresponding primes).

Programs

  • Mathematica
    Table[k = 2; While[p = k^n - 2; ! PrimeQ[p], k++]; p, {n, 20}] (* T. D. Noe, Apr 03 2012 *)

Extensions

a(2) corrected by Zak Seidov, Apr 03 2012

A095303 Smallest number k such that k^n - 2 is prime.

Original entry on oeis.org

4, 2, 9, 3, 3, 3, 7, 7, 3, 21, 9, 7, 19, 5, 7, 39, 15, 61, 15, 19, 21, 3, 19, 17, 21, 5, 21, 7, 85, 17, 7, 21, 511, 27, 27, 59, 3, 19, 91, 45, 3, 29, 321, 65, 9, 379, 69, 125, 49, 5, 9, 45, 289, 341, 61, 89, 171, 171, 139, 21, 139, 75, 25, 49, 15, 51, 57, 175, 31, 137, 147, 25, 441
Offset: 1

Views

Author

Hugo Pfoertner, Jun 01 2004

Keywords

Comments

The Bunyakovsky conjecture implies a(n) exists for all n. - Robert Israel, Jul 15 2018
Some of the results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 16 2019

Examples

			a(1) = 4 because 4^1 - 2 = 2 is prime, a(3) = 9 because 3^3 - 2 = 25, 5^3 - 2 = 123 and 7^3 - 2 = 341 = 11 * 31 are composite, whereas 9^3 - 2 = 727 is prime.

Links

Crossrefs

Cf. A095304 (corresponding primes), A087576 (smallest k such that k^n+2 is prime), A095302 (corresponding primes).
Cf. A014224.

Programs

  • Maple
    f:= proc(n) local k;
  for k from 3 by 2 do
    if isprime(k^n-2) then return k fi
  od
end proc:
f(1):= 4: f(2):= 2:
map(f, [$1..100]); # Robert Israel, Jul 15 2018
  • Mathematica
    a095303[n_] := For[k = 1, True, k++, If[PrimeQ[k^n - 2], Return[k]]]; Array[a095303, 100] (* Jean-François Alcover, Mar 01 2019 *)
  • PARI
    for (n=1,73,for(k=1,oo,if(isprime(k^n-2),print1(k,", ");break))) \\ Hugo Pfoertner, Oct 28 2018

Extensions

a(2) and a(46) corrected by T. D. Noe, Apr 03 2012
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.