%I #34 Sep 08 2022 08:46:11

%S 8,10,11,15,16,20,26,27,28,31,33,36,37,40,41,43,44,45,46,49,53,54,55,

%T 57,58,59,61,64,67,68,71,73,74,75,77,78,80,83,88,89,91,92,93,95,98,

%U 101,103,105,106,107,108,111,112,113,114,116,117,118,120,121,123

%N Numbers n such that 2n^2+2n+1, 3n^2+6n+5, 6n^2+30n+55 are all composite.

%C Or numbers n such that n^2 + (n+1)^2 + ... + (n+k)^2 is composite for all k>=0.

%C For a generalization see comment in A256581.

%t Select[Range[2, 200], !PrimeQ[2 #^2 + 2 # + 1] && !PrimeQ[3 #^2 + 6 # + 5] && !PrimeQ[6 #^2 + 30 # + 55] &] (* _Vincenzo Librandi_, Apr 01 2015 *)

%t Select[Range[200],AllTrue[{2#^2+2#+1,3#^2+6#+5,6#^2+30#+55},CompositeQ]&] (* _Harvey P. Dale_, Jul 15 2021 *)

%o (Magma) [n: n in [0..130] | not IsPrime(2*n^2+2*n+1) and not IsPrime(3*n^2+6*n+5) and not IsPrime(6*n^2+30*n+55)]; // _Vincenzo Librandi_, Apr 01 2015

%Y Cf. A000290, A001844, A005918, A027865, A089306, A077654, A256546, A256581.

%K nonn,easy

%O 1,1

%A _Vladimir Shevelev_, Mar 31 2015

%E More terms from _Peter J. C. Moses_, Mar 31 2015