login
A105571
Numbers m such that m - 2 and m + 2 are semiprimes.
10
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
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Apr 14 2005
STATUS
approved