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Numbers having evil number of 1's in their binary representation.
2

%I #26 Jul 24 2023 02:36:02

%S 0,7,11,13,14,19,21,22,25,26,28,31,35,37,38,41,42,44,47,49,50,52,55,

%T 56,59,61,62,63,67,69,70,73,74,76,79,81,82,84,87,88,91,93,94,95,97,98,

%U 100,103,104,107,109,110,111,112,115,117,118,119,121,122,123,124,125,126,131

%N Numbers having evil number of 1's in their binary representation.

%C A000120(a(n)) is in A001969.

%C Except for 0, the first term in which the sequence differs from A075930 is the 27th: a(27) = 63.

%C Also a(27) = 63 is the first odd term that is not in A092246. - _Altug Alkan_, Mar 18 2018

%H Robert Israel, <a href="/A235336/b235336.txt">Table of n, a(n) for n = 0..10000</a>

%e 7 in binary has 3 1's and since 3 is evil (i.e., belongs to A001969), then 7 is in the sequence.

%p filter:= n ->

%p convert(convert(convert(convert(n,base,2),`+`),base,2),`+`)::even:

%p select(filter, [$0..131]); # _Robert Israel_, Mar 18 2018

%t Select[Range[0, 150], EvenQ[DigitCount[DigitCount[#, 2, 1], 2, 1]] &] (* _Amiram Eldar_, Jul 24 2023 *)

%Y Cf. A000120, A001969, A075930, A092246.

%K nonn,base

%O 0,2

%A _Vladimir Shevelev_, Jan 06 2014