A105571 Numbers m such that m - 2 and m + 2 are semiprimes.

8, 12, 23, 24, 36, 37, 53, 60, 67, 84, 89, 93, 113, 117, 120, 121, 131, 143, 144, 157, 185, 203, 204, 207, 211, 215, 216, 217, 219, 251, 276, 289, 293, 297, 300, 301, 303, 307, 321, 325, 337, 360, 363, 379, 384, 393, 396, 405, 409, 413, 415, 449, 456, 471, 480

Offset

1,1

Comments

A001222(a(n)-2) = A001222(a(n)+2) = 2.

The even members of the sequence are A054735. - Robert Israel, Jan 18 2015

The prime members of the sequence are A063643. - Michel Marcus, Mar 27 2015

Links

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

Example

From Jon E. Schoenfield, Jan 18 2015: (Start)
12 - 2 = 10 = 2*5 and 12 + 2 = 14 = 2*7 so 12 is in the sequence.
23 - 2 = 21 = 3*7 and 23 + 2 = 25 = 5*5 so 23 is in the sequence.
16 - 2 = 14 = 2*7 but 16 + 2 = 18 = 2*3*3 so 16 is not in the sequence.
(End)

Maple

select(n -> numtheory:-bigomega(n+2) = 2 and numtheory:-bigomega(n-2) = 2,
[$1..1000]); # Robert Israel, Jan 18 2015

Mathematica

q=2; lst={}; Do[If[Plus@@Last/@FactorInteger[n-q]==q&&Plus@@Last/@FactorInteger[n+q]==q, AppendTo[lst, n]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 01 2009 *)
Select[Range[700], PrimeOmega[# + 2] == PrimeOmega[# - 2] == 2 &] (* Vincenzo Librandi, Mar 30 2015 *)

Prog

(Magma) IsSemiprime:=func< n | &+[k[2]: k in Factorization(n)] eq 2 >; [ n: n in [3..700] | IsSemiprime(n+2) and IsSemiprime(n-2) ]; // Vincenzo Librandi, Mar 30 2015
(Haskell)
a105571 n = a105571_list !! (n-1)
a105571_list = [x | x <- [3..], a064911 (x - 2) == 1, a064911 (x + 2) == 1]
-- Reinhard Zumkeller, Mar 31 2015

Crossrefs

Cf. A014574, A054735, A063643, A105572, A105573.

Cf. A064911.

Sequence in context: A072902 A269705 A189322 * A350633 A141616 A368549

Adjacent sequences: A105568 A105569 A105570 * A105572 A105573 A105574

Keyword

nonn

Author

Reinhard Zumkeller, Apr 14 2005

Status

approved