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%I #17 Mar 25 2021 04:52:27
%S 33,85,93,141,185,201,213,217,253,265,285,301,321,393,445,453,469,481,
%T 517,533,553,581,589,609,633,669,697,705,713,753,777,789,793,805,813,
%U 869,893,897,901,913,921,933,957,985,993,1001,1005,1041,1045,1065,1113
%N Numbers k such that k, k+1 and k+2 are nonprime and squarefree.
%C k-1 and k+3 are not squarefree. Proof: k is odd, otherwise k or k+2 would be divisible by 4. Thus k+1 is even and not divisible by 4, hence k-1 and k+3 are divisible by 4.
%H Amiram Eldar, <a href="/A073251/b073251.txt">Table of n, a(n) for n = 1..10000</a>
%t f[upto_]:=Module[{pp=PrimePi[upto],n},lst=Partition[Complement[Range[upto], Prime[Range[pp]]],3,1];Transpose[Select[lst,And@@SquareFreeQ/@#&]][[1]]]; f[1200] (* _Harvey P. Dale_, Mar 21 2011 *)
%o (PARI) isok1(k) = !isprime(k) && issquarefree(k); \\ A000469
%o isok(k) = isok1(k) && isok1(k+1) && isok1(k+2); \\ _Michel Marcus_, Mar 25 2021
%Y Cf. A000469, A005117, A007675, A073249, A073250, A121495.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Jul 22 2002
%E Edited by _Klaus Brockhaus_, Aug 07 2006
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