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A115393 Numbers n such that n, n-1 and n-2 are semiprimes.

%I A115393 #10 Jun 11 2020 23:26:44
%S A115393 35,87,95,123,143,203,215,219,303,395,447,635,699,843,923,1043,1139,
%T A115393 1263,1347,1403,1643,1763,1839,1895,1943,1983,2103,2183,2219,2307,
%U A115393 2363,2435,2463,2519,2643,2723,2735,3099,3387,3603,3695,3867,3903,3959,4287
%N A115393 Numbers n such that n, n-1 and n-2 are semiprimes.
%H A115393 Robert Israel, <a href="/A115393/b115393.txt">Table of n, a(n) for n = 1..10000</a>
%F A115393 a(n)=A056809(n)+2=A086005(n)+1=2*A086006(n)+1.
%p A115393 filter:= proc(n) local k;
%p A115393    k:= n mod 3;
%p A115393    if k = 0 then isprime(n/3) and isprime((n-1)/2) and numtheory:-bigomega(n-2)=2
%p A115393    elif k= 1 then false
%p A115393    else isprime((n-2)/3) and isprime((n-1)/2) and numtheory:-bigomega(n)=2
%p A115393    fi
%p A115393 end proc:
%p A115393 select(filter, [seq(i,i=3..10000,4)]); # _Robert Israel_, Jun 11 2020
%t A115393 upto=5000;p=Prime[Range[PrimePi[upto/2]]];lim=Floor[Sqrt[upto]]; sp={};k=0; While[k++;p[[k]]<=lim,sp=Join[sp,p[[k]] *Take[p,{k,PrimePi[upto/p[[k]]]}]]]; sp=Sort[sp];Transpose[Select [Partition[sp,3,1], Last[#]-#[[2]]==#[[2]]-First[#]==1&]][[3]] (* _Harvey P. Dale_, Mar 21 2011 -- semiprime generating portion of program from A001358 *)
%Y A115393 Cf. A056809, A086005, A086006.
%K A115393 nonn
%O A115393 1,1
%A A115393 _Zak Seidov_, Mar 08 2006