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

%I A166000 #22 Aug 14 2024 11:38:54
%S A166000 12253,14747,65173,83003,93253,95747,109139,147253,176747,213349,
%T A166000 255253,282253,284747,287437,305267,311747,315517,336253,338747,
%U A166000 364699,365747,444253,452579,471253,525253,554747,583789,633253,716747,741253,743747
%N A166000 Primes p such that p-5, p-3, p+3, and p+5 are divisible by cubes.
%C A166000 Subsequence of A089201. - _R. J. Mathar_, Dec 08 2015
%C A166000 Contains all primes == 12253 (mod 27000), and therefore the sequence is infinite. - _Robert Israel_, Apr 21 2016
%H A166000 G. C. Greubel, <a href="/A166000/b166000.txt">Table of n, a(n) for n = 1..16574</a>
%p A166000 filter:= proc(p) local d;
%p A166000   if not isprime(p) then return false fi;
%p A166000   for d in [-5,-3,3,5] do
%p A166000      if max(map(t -> t[2], ifactors(p+d)[2])) < 3 then return false fi;
%p A166000   od;
%p A166000   true
%p A166000 end proc:
%p A166000 select(filter, [seq(t,t=7..10^6,2)]); # _Robert Israel_, Apr 21 2016
%p A166000 # alternative
%p A166000 isA166000 := proc(n)
%p A166000     if isprime(n) then
%p A166000             isA046099(n-3) and isA046099(n+3) and isA046099(n-5) and isA046099(n+5) ;
%p A166000     else
%p A166000             false;
%p A166000     end if;
%p A166000 end proc: # _R. J. Mathar_, Aug 14 2024
%t A166000 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
%o A166000 (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 */
%Y A166000 Cf. A089201, A086708, A086709, A089212, A046099.
%K A166000 nonn
%O A166000 1,1
%A A166000 _Vladimir Joseph Stephan Orlovsky_, Oct 03 2009