%I #37 Sep 21 2024 17:58:43

%S 271,487,593,751,809,919,1249,1567,1783,1889,1999,2647,2663,2753,2969,

%T 3079,3511,3617,3727,3833,3943,4049,4159,4481,4591,4751,4801,5023,

%U 6857,6967,7937,8263,8369,9127,9343,10289,10313,10529,10639,11071,11177

%N Primes p such that p-1 and p+1 are both divisible by cubes (other than 1).

%H Robert Israel, <a href="/A086708/b086708.txt">Table of n, a(n) for n = 1..10000</a>

%F {p in A000040: p+1 in A046099 and p-1 in A046099}. - _R. J. Mathar_, Dec 08 2015

%F A089199 INTERSECT A089200. - _R. J. Mathar_, Dec 08 2015

%p isA086708 := proc(n)

%p if isprime(n) then

%p isA046099(n-1) and isA046099(n+1) ;

%p else

%p false;

%p end if;

%p end proc:

%p n := 1:

%p for c from 1 to 50000 do

%p if isA086708(c) then

%p printf("%d %d\n",n,c) ;

%p n := n+1 ;

%p end if;

%p end do: # _R. J. Mathar_, Dec 08 2015

%p Res:= NULL: count:= 0:

%p p:= 1:

%p while count < 100 do

%p p:= nextprime(p);

%p if max(seq(t[2],t=ifactors(p-1)[2]))>=3 and max(seq(t[2],t=ifactors(p+1)[2]))>=3 then

%p count:= count+1; Res:= Res, p;

%p fi

%p od:

%p Res; # _Robert Israel_, Jul 11 2018

%t f[n_]:=Max[Last/@FactorInteger[n]]; lst={};Do[p=Prime[n];If[f[p-1]>=3&&f[p+1]>=3,AppendTo[lst,p]],{n,6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Oct 03 2009 *)

%t dbcQ[p_]:=AnyTrue[Surd[#,3]&/@Rest[Divisors[p-1]],IntegerQ]&&AnyTrue[Surd[#,3]&/@Rest[ Divisors[ p+1]],IntegerQ]; Select[ Prime[Range[1500]],dbcQ] (* _Harvey P. Dale_, Sep 21 2024 *)

%o (PARI)

%o \\ Input no. of iterations n, power p and number to subtract and add k.

%o powerfreep4(n,p,k) = { c=0; pc=0; forprime(x=2,n, pc++; if(!ispowerfree(x-k,p) && !ispowerfree(x+k,p), c++; print1(x","); ) ); print(); print(c","pc","c/pc+.0) }

%o ispowerfree(m,p1) = { flag=1; y=component(factor(m),2); for(i=1,length(y), if(y[i] >= p1,flag=0;break); ); return(flag) } \\ _Cino Hilliard_, Dec 08 2003

%Y Cf. A162870 (subsequence).

%K nonn

%O 1,1

%A _Jason Earls_ and _Amarnath Murthy_, Jul 28 2003

%E Definition clarified by _Harvey P. Dale_, Sep 21 2024