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
Keywords
Examples
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)
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Programs
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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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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
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Maple
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
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 *)
Comments