A157483 - OEIS

%I #15 Mar 21 2020 14:06:53

%S 19,29,43,51,67,69,77,115,171,173,187,189,237,243,245,267,274,283,285,

%T 291,317,344,355,386,403,405,411,424,427,429,435,437,476,507,597,603,

%U 604,605,638,653,664,669,723,763,776,787,789,846,891,893,907,926,963

%N Numbers k such that k-1 and k+1 are divisible by exactly 3 primes, counted with multiplicity.

%C 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

%H Charles R Greathouse IV, <a href="/A157483/b157483.txt">Table of n, a(n) for n = 1..10000</a>

%e 19 is a term: 19-1 = 18 = 2*3*3 and 19+1 = 20 = 2*2*5.

%p 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

%t q=3;lst={};Do[If[Plus@@Last/@FactorInteger[n-1]==q&&Plus@@Last/@FactorInteger[n+1]==q,AppendTo[lst,n]],{n,7!}];lst

%t Mean/@SequencePosition[PrimeOmega[Range[1000]],{3,_,3}] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Mar 21 2020 *)

%o (PARI) is(n)=bigomega(n-1)==3 && bigomega(n+1)==3 \\ _Charles R Greathouse IV_, Feb 05 2017

%Y Cf. A124936, A014612, A156028.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Mar 01 2009

%E More terms from _Emeric Deutsch_, Mar 03 2009