A087695 Numbers n such that n + 3 and n - 3 are both prime.

8, 10, 14, 16, 20, 26, 34, 40, 44, 50, 56, 64, 70, 76, 86, 100, 104, 106, 110, 134, 154, 160, 170, 176, 194, 196, 226, 230, 236, 254, 260, 266, 274, 280, 310, 314, 334, 350, 356, 370, 376, 386, 436, 446, 460, 464, 506, 544, 560, 566, 574, 590, 596

Offset

1,1

Comments

A010051(a(n)-3) * A010051(a(n)+3) = 1. - Reinhard Zumkeller, Nov 17 2015

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(n) = A046117(n) - 3.

Maple

ZL:=[]:for p from 1 to 600 do if (isprime(p) and isprime(p+6) ) then ZL:=[op(ZL), (p+(p+6))/2]; fi; od; print(ZL); # Zerinvary Lajos, Mar 07 2007

Mathematica

lst={}; Do[If[PrimeQ[n-3]&&PrimeQ[n+3], AppendTo[lst, n]], {n, 10^3}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 08 2008 *)
Select[Range[600], AllTrue[#+{3, -3}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 06 2015 *)

Prog

(Haskell)
a087695 n = a087695_list !! (n-1)
a087695_list = filter
   (\x -> a010051' (x - 3) == 1 && a010051' (x + 3) == 1) [2, 4 ..]
-- Reinhard Zumkeller, Nov 17 2015
(PARI) p=2; q=3; forprime(r=5, 1e3, if(q-p<7 && (q-p==6 || r-p==6), print1(p+3", ")); p=q; q=r) \\ Charles R Greathouse IV, May 22 2018

Crossrefs

Cf. A014574, A087678-A087683, A087696, A087697, A088763, A046117, A010051.

Sequence in context: A171689 A163628 A060864 * A322998 A368280 A262708

Adjacent sequences: A087692 A087693 A087694 * A087696 A087697 A087698

Keyword

easy,nonn

Author

Zak Seidov, Sep 27 2003

Status

approved