A125592 Evil numbers (A001969) multiplied by 2.

0, 6, 10, 12, 18, 20, 24, 30, 34, 36, 40, 46, 48, 54, 58, 60, 66, 68, 72, 78, 80, 86, 90, 92, 96, 102, 106, 108, 114, 116, 120, 126, 130, 132, 136, 142, 144, 150, 154, 156, 160, 166, 170, 172, 178, 180, 184, 190, 192, 198, 202, 204, 210, 212, 216, 222, 226, 228, 232, 238

Offset: 1

Author

Luis H. Gallardo and Johan Huisman, Jan 07 2007

Keywords

• nonn
• easy

Comments

Numbers n such that the Maple command genpoly(n,2,t) outputs a polynomial in F_2[t] that is divisible by t(t+1), where F_2 is the finite field with two elements. E.g. a(2)=10 since the polynomial genpoly(10,2,t)=t^3+t = t(t+1)(t+1) in F_2[t] is divisible by the polynomial t(t+1) in F_2[t]

These are the even evil numbers: the intersection of A001968 and A005843. - Tanya Khovanova, May 04 2007

Programs

Mathematica

2*Select[Range[0,120],EvenQ[DigitCount[#,2,1]]&] (* Harvey P. Dale, Jun 14 2017 *)

PARI

is(n)=n%2==0 && hammingweight(n)%2==0 \\ Charles R Greathouse IV, Mar 22 2013

PARI

a(n)=4*n--+hammingweight(n)%2*2 \\ Charles R Greathouse IV, Mar 22 2013