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A105571
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Numbers m such that m - 2 and m + 2 are semiprimes.
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10
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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EXAMPLE
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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)
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MAPLE
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select(n -> numtheory:-bigomega(n+2) = 2 and numtheory:-bigomega(n-2) = 2,
[$1..1000]); # Robert Israel, Jan 18 2015
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A014574, A054735, A063643, A105572, A105573.
Cf. A064911.
Sequence in context: A072902 A269705 A189322 * A350633 A141616 A326994
Adjacent sequences: A105568 A105569 A105570 * A105572 A105573 A105574
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Apr 14 2005
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STATUS
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approved
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