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Numbers that have an even number of 0's and 1's in their binary expansion.
4

%I #23 Aug 16 2021 13:43:28

%S 3,9,10,12,15,33,34,36,39,40,43,45,46,48,51,53,54,57,58,60,63,129,130,

%T 132,135,136,139,141,142,144,147,149,150,153,154,156,159,160,163,165,

%U 166,169,170,172,175,177,178,180,183,184,187,189,190,192,195,197,198

%N Numbers that have an even number of 0's and 1's in their binary expansion.

%C Intersection of A001969 and A059010.

%H Indranil Ghosh, <a href="/A059012/b059012.txt">Table of n, a(n) for n = 1..32768</a>

%e 36 is in the sequence because 36 = 100100_10. '100100' has two 1's and four 0's. - _Indranil Ghosh_, Feb 10 2017

%t Select[Range[200],AllTrue[{DigitCount[#,2,0],DigitCount[#,2,1]},EvenQ]&] (* _Harvey P. Dale_, Aug 16 2021 *)

%o (PARI) is(n)=hammingweight(n)%2==0 && hammingweight(bitneg(n, #binary(n)))%2==0 \\ _Charles R Greathouse IV_, Mar 26 2013

%o (Python)

%o i=0

%o j=1

%o while j<=300:

%o if bin(i)[2:].count("1")%2 == 0 == bin(i)[2:].count("0")%2:

%o print(str(j)+" "+str(i))

%o j+=1

%o i+=1 # _Indranil Ghosh_, Feb 10 2017

%Y Cf. A000069, A001969, A059009-A059014.

%K nonn,base,easy

%O 1,1

%A _Patrick De Geest_, Dec 15 2000