A089201 Primes p such that p-3 and p+3 are divisible by a cube.

683, 1747, 2659, 3253, 4253, 4397, 7253, 7549, 8747, 9829, 10253, 12253, 13037, 14747, 16253, 16747, 17747, 18253, 18637, 19891, 20747, 21269, 23747, 25253, 25747, 27253, 28123, 29501, 30253, 31253, 34253, 34603, 34747, 35747, 37253

Offset: 1

Author

Cino Hilliard, Dec 08 2003

Keywords

• easy
• nonn

Examples

			683-3=2^3*5*17,683+3=2*7^3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..330 from R. J. Mathar)

Crossrefs

Cf. A046099.

Programs

Maple

isA089201 := proc(n)
    if isprime(n) then
        isA046099(n-3) and isA046099(n+3) ;
    else
        false;
    end if;
end proc: # R. J. Mathar, Dec 08 2015

Mathematica

Select[Prime[Range[4000]],Max[Transpose[FactorInteger[#-3]][[2]]]>2 && Max[ Transpose[FactorInteger[#+3]][[2]]]>2&] (* Harvey P. Dale, Jan 26 2013 *)

PARI

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) }
ispowerfree(m,p1) = { flag=1; y=component(factor(m),2); for(i=1,length(y), if(y[i] >= p1,flag=0;break); ); return(flag) }

Formula

{p in A000040: p+3 in A046099 and p-3 in A046099}. - R. J. Mathar, Dec 08 2015