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

1,1

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

Formula

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

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 *)

Crossrefs

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

Sequence in context: A357500 A158891 A213220 * A371303 A249333 A372934

Adjacent sequences: A087677 A087678 A087679 * A087681 A087682 A087683

Keyword

easy,nonn

Author

Zak Seidov, Sep 27 2003

Extensions

More terms from Ray Chandler, Oct 26 2003

Status

approved