A049282 Primes p such that both p-2 and p+2 are squarefree.

3, 5, 13, 17, 19, 31, 37, 41, 53, 59, 67, 71, 89, 103, 107, 109, 113, 131, 139, 157, 163, 179, 181, 193, 197, 199, 211, 229, 233, 239, 251, 257, 269, 271, 283, 293, 307, 311, 337, 347, 379, 383, 397, 401, 409, 419, 431, 433, 449, 463, 467, 487, 491, 499, 503

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Examples

			37 is here because neither 37+2 nor 37-2 is divisible by squares.
		

Links

• John Cerkan, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A049231, A049233.

Programs

Maple

with(numtheory): A049282:=n->`if`(isprime(n) and issqrfree(n-2) and issqrfree(n+2), n, NULL): seq(A049282(n), n=1..10^3); # Wesley Ivan Hurt, Jun 25 2016

Mathematica

lst={}; Do[p=Prime[n]; If[SquareFreeQ[p-2]&&SquareFreeQ[p+2], AppendTo[lst,p]], {n,6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 20 2008 *)
Select[Prime[Range[100]],AllTrue[#+{2,-2},SquareFreeQ]&] (* Harvey P. Dale, Apr 18 2025 *)

PARI

lista(nn) = forprime(p=2, nn, if (issquarefree(p-2) && issquarefree(p+2), print1(p, ", "))); \\ Michel Marcus, Jun 22 2016

Formula

Intersection of A049231 and A049233.