A061673 Even numbers k such that k+1 and k-1 are both composite.

26, 34, 50, 56, 64, 76, 86, 92, 94, 116, 118, 120, 122, 124, 134, 142, 144, 146, 154, 160, 170, 176, 184, 186, 188, 202, 204, 206, 208, 214, 216, 218, 220, 236, 244, 246, 248, 254, 260, 266, 274, 286, 288, 290, 296, 298, 300, 302, 304, 320, 322, 324, 326

Offset: 1

Author

Enoch Haga, Jun 16 2001

Keywords

• easy
• nonn
• nice

Comments

If a(n + 1) > a(n) + 2 then a(n) + 3 and a(n + 1) - 3 are both prime. - Joseph Wheat, Mar 16 2025

Examples

			a(3)=50 because 50 - 1 = 49 and 50 + 1 = 51 and both 49 and 51 are composite.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Twin Composites

Crossrefs

Cf. A014574, A055670.

A025583(n-1) - 1.

Programs

GAP

Filtered([0,2..340],n->not IsPrime(n-1) and not IsPrime(n+1)); # Muniru A Asiru, Jul 01 2018;

Haskell

a061673 n = a061673_list !! (n-1)
a061673_list = filter bothComp [4,6..] where
   bothComp n = (1 - a010051 (n-1)) * (1 - a010051 (n+1)) > 0
-- Reinhard Zumkeller, Feb 27 2011

Mathematica

fQ[n_] := !PrimeQ[n - 1] && !PrimeQ[n + 1]; Select[2 Range@ 163, fQ]
Select[Range[2,400,2],AllTrue[#+{1,-1},CompositeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 01 2014 *)
2*SequencePosition[Table[If[CompositeQ[n],1,0],{n,1,351,2}],{1,1}][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 04 2020 *)

PARI

{ n=0; forstep (a=2, 3986, 2, if (!isprime(a+1) && !isprime(a-1), write("b061673.txt", n++, " ", a)) ) } \\ Harry J. Smith, Jul 26 2009

Python

from sympy import isprime
def abelow(limit):
  for k in range(2, limit, 2):
    if not isprime(k-1) and not isprime(k+1): yield k
print([an for an in abelow(327)]) # Michael S. Branicky, Jan 02 2021