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

Author

Zak Seidov, Sep 27 2003

Keywords

• nonn
• easy

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

Crossrefs

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

Programs

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 *)

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

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

Extensions

More terms from Ray Chandler, Oct 26 2003