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

Author

Vladimir Joseph Stephan Orlovsky, Oct 03 2009

Keywords

• nonn

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

Crossrefs

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

Programs

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
# alternative
isA166000 := proc(n)
    if isprime(n) then
            isA046099(n-3) and isA046099(n+3) and isA046099(n-5) and isA046099(n+5) ;
    else
            false;
    end if;
end proc: # R. J. Mathar, Aug 14 2024

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

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 */