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

1,1

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

Formula

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

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 *)

Prog

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

Crossrefs

Essentially the same as A087679.

Sequence in context: A336115 A072569 A072572 * A125215 A102739 A124622

Adjacent sequences: A029705 A029706 A029707 * A029709 A029710 A029711

Keyword

nonn

Author

N. J. A. Sloane

Status

approved