A087680 Numbers n such that n + 4 and n - 4 are both prime.

7, 9, 15, 27, 33, 57, 63, 75, 93, 105, 135, 153, 177, 195, 237, 267, 273, 363, 393, 405, 435, 453, 483, 495, 567, 573, 597, 603, 657, 687, 705, 723, 747, 765, 825, 915, 933, 987, 1017, 1035, 1065, 1113, 1167, 1197, 1227, 1233, 1287, 1293, 1323, 1377, 1443

Offset: 1

Author

Zak Seidov, Sep 27 2003

Keywords

• easy
• nonn

Comments

All terms > 7 (prime) are divisible by 3. Also note that n-4 and n+4 are not necessarily consecutive primes. First case when n-4 and n+4 are consecutive primes is for n=93 with n-4=89 and n+4=97. - Zak Seidov, Apr 22 2015

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A023202, A014574, A087678-A087683, A087695-A087697, A088764.

Programs

Maple

ZL:=[]:for p from 1 to 1444 do if (isprime(p) and isprime(p+8) ) then ZL:=[op(ZL),(p+(p+8))/2]; fi; od; print(ZL); # Zerinvary Lajos, Mar 07 2007

Mathematica

f[n_]:=PrimeQ[n-4]&&PrimeQ[n+4]; lst={};Do[If[f[n],AppendTo[lst,n]],{n,3,8!,2}];lst (* Vladimir Joseph Stephan Orlovsky, Oct 09 2009 *)
Select[Prime[Range[250]],PrimeQ[#+8]&]+4 (* Harvey P. Dale, May 21 2023 *)

Formula

a(n) = A023202(n) + 4. - Michel Marcus, Apr 22 2015

Extensions

More terms from Ray Chandler, Oct 26 2003