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Numbers k such that k and k+1 are composite and squarefree.
5

%I #7 Feb 22 2021 03:15:25

%S 14,21,33,34,38,57,65,69,77,85,86,93,94,105,110,114,118,122,129,133,

%T 141,142,145,154,158,165,177,182,185,186,194,201,202,205,209,213,214,

%U 217,218,221,230,237,246,253,254,258,265,266,273,285,286,290,298,301,302

%N Numbers k such that k and k+1 are composite and squarefree.

%C Numbers that are in A068780 and in A007674.

%H Amiram Eldar, <a href="/A121495/b121495.txt">Table of n, a(n) for n = 1..10000</a>

%e 21 = 3*7 and 22 = 2*11 are squarefree, so 21 is in the sequence.

%t q[n_] := CompositeQ[n] && SquareFreeQ[n]; Select[Range[300], q[#] && q[# + 1] &] (* _Amiram Eldar_, Feb 22 2021 *)

%o (PARI) for(n=1,310,if(!isprime(n)&&!isprime(n+1)&&issquarefree(n)&&issquarefree(n+1),print1(n,",")))

%Y Cf. A002808, A005117, A007674, A068780.

%K easy,nonn

%O 1,1

%A _Klaus Brockhaus_, Aug 03 2006