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Numbers k such that 6k-5 and 6k-1 are both composite.
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%I #29 Mar 20 2023 12:34:17

%S 16,20,21,35,37,50,51,54,55,61,66,68,76,79,81,83,86,89,90,105,112,115,

%T 118,121,125,128,130,131,134,141,142,145,146,149,150,151,153,156,160,

%U 161,165,168,180,181,186,190,191,195,200,202,208,211,212,219,223

%N Numbers k such that 6k-5 and 6k-1 are both composite.

%t Select[Range[223], ! PrimeQ[6#-5] && ! PrimeQ[6#-1] &] (* _T. D. Noe_, Nov 09 2011 *)

%t Select[Range[250],AllTrue[6#+{-5,-1},CompositeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Oct 11 2018 *)

%o (Magma) [ n: n in [1..223] | not IsPrime(6*n-5) and not IsPrime(6*n-1) ]; // _Bruno Berselli_, Nov 09 2011

%o (PARI) for(n=1,1e3,if(!isprime(6*n-5)&&!isprime(6*n-1),print1(n", "))) \\ _Charles R Greathouse IV_, Nov 10 2011

%Y Cf. A186243.

%K nonn,easy

%O 1,1

%A _Eleonora Echeverri-Toro_, Nov 09 2011