A029708 Numbers k such that k-2 and k+2 are consecutive primes.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

All terms are multiples of 3. Minimal first difference is 6. - Zak Seidov, May 15 2013

Links

• Marius A. Burtea, Table of n, a(n) for n = 1..10548 (first 1000 terms from Zak Seidov )
• Zak Seidov, Table of n, a(n)/3 for n = 1..1000

Crossrefs

Essentially the same as A087679.

Programs

Magma

[k:k in [1..1500]| IsPrime(k-2) and NextPrime(k-2) eq k+2 ]; // Marius A. Burtea, Jan 24 2019

Mathematica

f[n_]:=PrimeQ[n-2]&&PrimeQ[n+2]; lst={};Do[If[f[n],AppendTo[lst,n]],{n,7,8!,2}];lst (* Vladimir Joseph Stephan Orlovsky, Oct 09 2009 *)
Select[Range[9,1432,6],PrimeQ[#-2]&&PrimeQ[#+2]&] (* Zak Seidov, May 15 2013 - just for terms in DATA *)
Mean/@Select[Partition[Prime[Range[300]],2,1],#[[2]]-#[[1]]==4&] (* Harvey P. Dale, Feb 15 2020 *)

Formula

a(n) = (A029710(n) + A031505(n+1))/2 = A029710(n) + 2 = A031505(n+1) - 2.