A166000 Primes p such that p-5, p-3, p+3, and p+5 are divisible by cubes.

12253, 14747, 65173, 83003, 93253, 95747, 109139, 147253, 176747, 213349, 255253, 282253, 284747, 287437, 305267, 311747, 315517, 336253, 338747, 364699, 365747, 444253, 452579, 471253, 525253, 554747, 583789, 633253, 716747, 741253, 743747

Offset

1,1

Comments

Subsequence of A089201. - R. J. Mathar, Dec 08 2015

Contains all primes == 12253 (mod 27000), and therefore the sequence is infinite. - Robert Israel, Apr 21 2016

Links

G. C. Greubel, Table of n, a(n) for n = 1..16574

Maple

filter:= proc(p) local d;
  if not isprime(p) then return false fi;
  for d in [-5, -3, 3, 5] do
     if max(map(t -> t[2], ifactors(p+d)[2])) < 3 then return false fi;
  od;
  true
end proc:
select(filter, [seq(t, t=7..10^6, 2)]); # Robert Israel, Apr 21 2016

Mathematica

f[n_]:=Max[Last/@FactorInteger[n]]; q=3; lst={}; Do[p=Prime[n]; If[f[p-5]>=q&&f[p-3]>=q&&f[p+3]>=q&&f[p+5]>=q, AppendTo[lst, p]], {n, 4*8!}]; lst

Prog

(PARI) ncf(n)={vecmax(factor(n)[, 2])>2}; forprime(p=5, 1e7, if(ncf(p+5)&&ncf(p+3)&&ncf(p-3)&&ncf(p-5), print1(p", "))) /* Charles R Greathouse IV, Oct 05 2009 */

Crossrefs

Cf. A089201, A086708, A086709, A089212, A046099.

Sequence in context: A338950 A204873 A135128 * A252500 A252497 A254548

Adjacent sequences: A165997 A165998 A165999 * A166001 A166002 A166003

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Oct 03 2009

Status

approved