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

%I A105571 #27 Sep 08 2022 08:45:17
%S A105571 8,12,23,24,36,37,53,60,67,84,89,93,113,117,120,121,131,143,144,157,
%T A105571 185,203,204,207,211,215,216,217,219,251,276,289,293,297,300,301,303,
%U A105571 307,321,325,337,360,363,379,384,393,396,405,409,413,415,449,456,471,480
%N A105571 Numbers m such that m - 2 and m + 2 are semiprimes.
%C A105571 A001222(a(n)-2) = A001222(a(n)+2) = 2.
%C A105571 The even members of the sequence are A054735. - _Robert Israel_, Jan 18 2015
%C A105571 The prime members of the sequence are A063643. - _Michel Marcus_, Mar 27 2015
%H A105571 Reinhard Zumkeller, <a href="/A105571/b105571.txt">Table of n, a(n) for n = 1..10000</a>
%e A105571 From _Jon E. Schoenfield_, Jan 18 2015: (Start)
%e A105571 12 - 2 = 10 = 2*5 and 12 + 2 = 14 = 2*7 so 12 is in the sequence.
%e A105571 23 - 2 = 21 = 3*7 and 23 + 2 = 25 = 5*5 so 23 is in the sequence.
%e A105571 16 - 2 = 14 = 2*7 but 16 + 2 = 18 = 2*3*3 so 16 is not in the sequence.
%e A105571 (End)
%p A105571 select(n -> numtheory:-bigomega(n+2) = 2 and numtheory:-bigomega(n-2) = 2,
%p A105571 [$1..1000]); # _Robert Israel_, Jan 18 2015
%t A105571 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 *)
%t A105571 Select[Range[700], PrimeOmega[# + 2] == PrimeOmega[# - 2] == 2 &] (* _Vincenzo Librandi_, Mar 30 2015 *)
%o A105571 (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
%o A105571 (Haskell)
%o A105571 a105571 n = a105571_list !! (n-1)
%o A105571 a105571_list = [x | x <- [3..], a064911 (x - 2) == 1, a064911 (x + 2) == 1]
%o A105571 -- _Reinhard Zumkeller_, Mar 31 2015
%Y A105571 Cf. A014574, A054735, A063643, A105572, A105573.
%Y A105571 Cf. A064911.
%K A105571 nonn
%O A105571 1,1
%A A105571 _Reinhard Zumkeller_, Apr 14 2005