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A157483
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Numbers k such that k-1 and k+1 are divisible by exactly 3 primes, counted with multiplicity.
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7
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19, 29, 43, 51, 67, 69, 77, 115, 171, 173, 187, 189, 237, 243, 245, 267, 274, 283, 285, 291, 317, 344, 355, 386, 403, 405, 411, 424, 427, 429, 435, 437, 476, 507, 597, 603, 604, 605, 638, 653, 664, 669, 723, 763, 776, 787, 789, 846, 891, 893, 907, 926, 963
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OFFSET
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1,1
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COMMENTS
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Omega(a(n) - 1) = Omega(a(n) + 1) = 3, where Omega(n)=A001222(n). In general twin k-almost prime pairs are defined by Omega(a(n) - 1) = Omega(a(n) + 1) = k. Twin 1-almost primes are twin prime pairs (A014574). - Redjan Shabani, Jul 20 2012
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LINKS
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EXAMPLE
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19 is a term: 19-1 = 18 = 2*3*3 and 19+1 = 20 = 2*2*5.
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MAPLE
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with(numtheory); a := proc (n) if bigomega(n-1) = 3 and bigomega(n+1) = 3 then n else end if end proc: seq(a(n), n = 2 .. 1100); # Emeric Deutsch, Mar 03 2009
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MATHEMATICA
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q=3; lst={}; Do[If[Plus@@Last/@FactorInteger[n-1]==q&&Plus@@Last/@FactorInteger[n+1]==q, AppendTo[lst, n]], {n, 7!}]; lst
Mean/@SequencePosition[PrimeOmega[Range[1000]], {3, _, 3}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 21 2020 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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