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Primes p such that p-5, p-3, p+3, and p+5 are divisible by cubes.
4

%I #22 Aug 14 2024 11:38:54

%S 12253,14747,65173,83003,93253,95747,109139,147253,176747,213349,

%T 255253,282253,284747,287437,305267,311747,315517,336253,338747,

%U 364699,365747,444253,452579,471253,525253,554747,583789,633253,716747,741253,743747

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

%C Subsequence of A089201. - _R. J. Mathar_, Dec 08 2015

%C Contains all primes == 12253 (mod 27000), and therefore the sequence is infinite. - _Robert Israel_, Apr 21 2016

%H G. C. Greubel, <a href="/A166000/b166000.txt">Table of n, a(n) for n = 1..16574</a>

%p filter:= proc(p) local d;

%p if not isprime(p) then return false fi;

%p for d in [-5,-3,3,5] do

%p if max(map(t -> t[2], ifactors(p+d)[2])) < 3 then return false fi;

%p od;

%p true

%p end proc:

%p select(filter, [seq(t,t=7..10^6,2)]); # _Robert Israel_, Apr 21 2016

%p # alternative

%p isA166000 := proc(n)

%p if isprime(n) then

%p isA046099(n-3) and isA046099(n+3) and isA046099(n-5) and isA046099(n+5) ;

%p else

%p false;

%p end if;

%p end proc: # _R. J. Mathar_, Aug 14 2024

%t 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 (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 Cf. A089201, A086708, A086709, A089212, A046099.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Oct 03 2009