A256385 Numbers n such that 2n^2+2n+1, 3n^2+6n+5, 6n^2+30n+55 are all composite.

8, 10, 11, 15, 16, 20, 26, 27, 28, 31, 33, 36, 37, 40, 41, 43, 44, 45, 46, 49, 53, 54, 55, 57, 58, 59, 61, 64, 67, 68, 71, 73, 74, 75, 77, 78, 80, 83, 88, 89, 91, 92, 93, 95, 98, 101, 103, 105, 106, 107, 108, 111, 112, 113, 114, 116, 117, 118, 120, 121, 123

Offset: 1

Author

Vladimir Shevelev, Mar 31 2015

Keywords

• nonn
• easy

Comments

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

For a generalization see comment in A256581.

Crossrefs

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

Programs

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

Mathematica

Select[Range[2, 200], !PrimeQ[2 #^2 + 2 # + 1] && !PrimeQ[3 #^2 + 6 # + 5] && !PrimeQ[6 #^2 + 30 # + 55] &] (* Vincenzo Librandi, Apr 01 2015 *)
Select[Range[200],AllTrue[{2#^2+2#+1,3#^2+6#+5,6#^2+30#+55},CompositeQ]&] (* Harvey P. Dale, Jul 15 2021 *)

Extensions

More terms from Peter J. C. Moses, Mar 31 2015