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

1,1

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.

Links

Table of n, a(n) for n=1..61.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A006757 A265200 A126803 * A274560 A122990 A288107

Adjacent sequences: A256382 A256383 A256384 * A256386 A256387 A256388

Keyword

nonn,easy

Author

Vladimir Shevelev, Mar 31 2015

Extensions

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

Status

approved