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%I #33 Jul 11 2018 20:13:00
%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.
%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 *)
%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
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