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A256385
Numbers n such that 2n^2+2n+1, 3n^2+6n+5, 6n^2+30n+55 are all composite.
5
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.
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
KEYWORD
nonn,easy
AUTHOR
Vladimir Shevelev, Mar 31 2015
EXTENSIONS
More terms from Peter J. C. Moses, Mar 31 2015
STATUS
approved