A087679 Numbers k such that both k+2 and k-2 are prime.

5, 9, 15, 21, 39, 45, 69, 81, 99, 105, 111, 129, 165, 195, 225, 231, 279, 309, 315, 351, 381, 399, 441, 459, 465, 489, 501, 615, 645, 675, 741, 759, 771, 825, 855, 861, 879, 885, 909, 939, 969, 1011, 1089, 1095, 1215, 1281, 1299, 1305, 1425, 1431, 1449, 1485

Offset

1,1

Comments

Essentially the same as A029708: a(n) = A029708(n-1) for n>=2.

Midpoint of cousin prime pairs.

The only prime is 5. All other terms are multiples of 3. - Zak Seidov, May 19 2014

Links

M. F. Hasler, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Cousin Primes

Formula

a(n) = (A023200(n) + A046132(n))/2 = A023200(n) + 2 = A046132(n) - 2.

a(n+1) = A056956(n)*6 + 3 = A157834(n)*3; a(n) = A088762(n)*2 + 1. - M. F. Hasler, Apr 05 2017

Maple

ZL:=[]:for p from 1 to 1485 do if (isprime(p) and isprime(p+4) ) then ZL:=[op(ZL), (p+(p+4))/2]; fi; od; print(ZL); # Zerinvary Lajos, Mar 07 2007

Mathematica

lst={}; Do[If[PrimeQ[n-2]&&PrimeQ[n+2], AppendTo[lst, n]], {n, 3, 8!, 2}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 14 2009 *)

Prog

(PARI) s=[]; for(n=1, 2000, if(isprime(n-2) && isprime(n+2), s=concat(s, n))); s \\ Colin Barker, May 19 2014
(PARI) is_A087679(n)={isprime(n-2) && isprime(n+2)} \\ For numbers >> 10^12 one should add conditions {n%6==3 && ... || n==5} or consider only such numbers congruent to 3 (mod 6). - M. F. Hasler, Apr 05 2017

Crossrefs

Cf. A014574, A087678-A087683, A087695-A087697, A088762.

Sequence in context: A315078 A315079 A217277 * A179187 A315080 A315081

Adjacent sequences: A087676 A087677 A087678 * A087680 A087681 A087682

Keyword

nonn,easy

Author

Zak Seidov, Sep 27 2003

Extensions

More terms from Ray Chandler, Oct 26 2003

Status

approved