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

35, 87, 95, 123, 143, 203, 215, 219, 303, 395, 447, 635, 699, 843, 923, 1043, 1139, 1263, 1347, 1403, 1643, 1763, 1839, 1895, 1943, 1983, 2103, 2183, 2219, 2307, 2363, 2435, 2463, 2519, 2643, 2723, 2735, 3099, 3387, 3603, 3695, 3867, 3903, 3959, 4287

Offset: 1

Author

Zak Seidov, Mar 08 2006

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A056809, A086005, A086006.

Programs

Maple

filter:= proc(n) local k;
   k:= n mod 3;
   if k = 0 then isprime(n/3) and isprime((n-1)/2) and numtheory:-bigomega(n-2)=2
   elif k= 1 then false
   else isprime((n-2)/3) and isprime((n-1)/2) and numtheory:-bigomega(n)=2
   fi
end proc:
select(filter, [seq(i,i=3..10000,4)]); # Robert Israel, Jun 11 2020

Mathematica

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 *)

Formula

a(n)=A056809(n)+2=A086005(n)+1=2*A086006(n)+1.