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

1,1

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Twin Composites

Example

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

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 *)

Prog

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

Crossrefs

Cf. A014574, A055670.

A025583(n-1) - 1.

Sequence in context: A100393 A133635 A167705 * A072571 A307033 A058763

Adjacent sequences: A061670 A061671 A061672 * A061674 A061675 A061676

Keyword

easy,nonn,nice

Author

Enoch Haga, Jun 16 2001

Status

approved